Reprinted from THE REVIEW OF SCIENTIFIC INSTRUMENTS, Vol. 22, No. 1, 1-29, January, 1951 Printed in U. S. A. Radio Telemetry M. H. NICHOLS AND L. L. RAUCH Department of Aeronautical Enginteering, University of Michigan, Ann Arbor, Michigan (Received September 25, 1950) I. Introduction IV-4.2. Recording Pulse Width Modulation ~~~~II.T N~~~~omenclature ^and Pulse Position Modulation with II. Nomenclature High Frequency Response III. Frequency Division Multiplexing in Radio IV-4.3. The Effect of Pulse Integration Telemetry IV-4.4. General Considerations III-1. CROSSTALK IN FREQUENCY DIVISION IV-5. PULSE CODE MODULATION FOR TELEM111-2. NOISE CHARACTERISTICS OF FREQUENCY ETRY DIVISION SYSTEMS IV-6. COMPARISON OF FLUCTUATION NOISE 111-3. OVERMODULATION VERSUS NOISE CHARACTERISTICS OF THE SYSTEMS IN 111-4. EFFECT OF MULTIPATH TRANSMISSION TABLE II ON THE BASIS OF EQUAL RADIO II-5. SUB-CARRIER MODULATION FREQUENCY BAND WIDTH III-6. CHOICE OF SUB-CARRIER FREQUENCIES -7. IMPULSE NOISE IN TIME DIVISIO 111I-7. CARRIER MODULATION 111-7. CARRIER MODULATION'IV-7.IMPULSE NOISE IN TIME DIVISION 111-8. IMPROVEMENT THRESHOLDS MUL XIN IV-7.1. Impulse Noise in PAM IV. Time Division in Radio Telemetry IV-7.2. Impulse Noise in PPM IV-1. FREQUENCY RESPONSE OF TIME DIVI- IV-7.3. Impulse Noise in PCM SION IV-8. SOME CONSIDERATIONS INVOLVED IN IV-I.1. Direct Recording of Pulse Amplitude THE CHOICE OF TYPE OF CARRIER MODUModulation LATION IN TIME DIVISION TELEMETRY IV-1.2. The Low Pass Filter with Pulse IV-9. TRIPLE MODULATION IN RADIO TELEMAmplitude Modulation ETRY IV-1.3. The Pulse Widener with Pulse IV-. MISCELLANEOUS REMARKS ON TIME Amplitude Modulation DIVISION MULTIPLEXING Amplitude Modulation IV-1.4. Pulse Width Modulation V. Comparison of Frequency Division and Time IV-2. CROSSTALK IN TIME DIVISION Division Multiplexing in Radio Telemetry IV-3. FLUCTUATION NOISE IN TIME DIVISION SYSTEMS V-1. COMPARISON OF CROSSTALK AND FLUCIV-3.1. Band-Width Requirements in PAM TUATION NOISE IV-3.2. Band-WidthConsiderationsinPWM V-2. COMPARISON OF COMPLEXITY AND REIV-3.3. Band-WidthConsiderationsinPPMAM VI. Instrumentation for Radio Telementry IV-3.4. Band-Width for PCM IV-3.4. Band-Width for PCM VI-1. RESISTANCE WIRE STRAIN GAUGE TYPE IV-4. FLUCTUATION NOISE CHARACTERISTICS OF INSTRUMENTATION OF SYSTEMS WHICH DO NOT USE THE VI-2. VARIABLE INDUCTANCE TYPE INSTRULOW PASS OUTPUT FILTER MENTATION IV-4.1. Recording Pulse Amplitude Modula- VI-3. POTENTIOMETER TYPE INSTRUMENTAtion with High Frequency Response TION VI-4. VOLTAGE TYPE INSTRUMENTS VI-5. MISCELLANEOUS REMARKS ON INSTRUMENTS I

2 M. H. NICHOLS AND L. L. RAUCH VII. Recording in Radio Telemetry quency spectrum, radio range, space, weight and power VII-1. AIRBORNE RECORDING available, expendability, etc. The purpose of this paper is to review and develop the underlying theory of radio VIII. Crosstalk from Overload in Frequency- telemetry to the point where it can be applied to the Division Multiplex Radio Links choice of method which is to satisfy these requirements VIII-1. CRITERION FOR TOLERABLE CROSSTALK and to the formulation of specifications for future deVIII-2. JUSTIFICATION OF THE CRITERION velopments. No attempt is made to cover techniques. X. Cro k De to Rtricd Bd Widh Since there is increasing use of airborne recording and IX. Crosstalk Due to Restricted Band Width in seamlk ue Modtrion i- since many of the principles involved in analysis of radio Pulse-Amplitude Modulation Multiplex Sys- telemetry apply to recording methods, Section VII on "^~~~~~~tems ~recording is included. No attempt will be made in this X. Information Efficiency of Pulse-Time Modula- paper to discuss the problems of propagation, antenna tion and Multiplex Methods design, etc. Although work on the material in this paper was I. Introduction started when the authors were employed on an NDRC project at Princeton University, the paper was comA LTHOUGH telemetry was developed some years pleted and written under the sponsorship of United ago for such things as remote metering in the States Air Force. This article was planned jointly by electrical power industry,(R5) the use of a radio link did both authors, but Sections I through VII and Appendix not become of real importance until the need for remote 1 were prepared principally by M. H. Nichols and metering arose in the field of high performance aircraft Sections VIII through X and Appendices 2 through 5 and rocket development and in the field of atmospheric prepared principally by L. L. Rauch. research. There are essentially two reasons why it is often necessary to resort to the use of radio telemetry, II. Nomenclature as opposed to airborne recording, for example. One ai =improvement threshold of the ith frequency reason is the difficulty of recovery of records from cer- modulated sub-carrier (measured at the video tain types of flights and the other is that in many cases output of the radio receiver). the limitations of space, weight, and operating condi- AM amplitude modulation. tions can be better met by radio telemetry. An ratio of the individual sub-carrier amplitude There are several features which distinguish radioal sub-c,P~~~~.c ~~ _.. ~~' ^ -(from a group of sinusoidal sub-carriers of telemetry from ordinary communication. One is the al ca o.. *~ *~'I ~ * it- * r ~ equal amplitude) which will cause oversevere limitation on space and weight and the rigor of...~~~~~..~~~ ^ ^modulation Pn of the time to the largest the operating conditions, particularly at the trans- m dulat of the time to the laret ~.. ~.^. ii.i~.i..~ l individual sub-carrier amplitude which will mitter, and another is the high signal-to-noise ratio. *,., a r * *... _,. cause no overmodulation at all. requirement which results from the precision required in metering. Also in many cases it is necessary to meter a =fully modulated amplitude of the th subcarrier. quantities which have very slowly varying components, cre which means that essentially DC response is required. aoi = unmodulated RMS amplitudeof th sub-carrier Almost every application of radio telemetry involves (measured at the video output of the radio some form of multiplexing-i.e., the transmission of receiver). several channels of information by the same radio a =a positive number used in connection with carrier. The high signal-to-noise requirement limits the PAM whose reciprocal, I/a, gives the fracamount of crosstalk that can be tolerated at any time. tion of the permissible time that an indiIn order to simplify reduction of the data, it is generally vidual channel is switched on. desirable for each channel to have essentially a linear Af = fraction of maximum possible pulse widening. response. Taken together, these features may place Cn =cumulative probability function for sum of n severe requirements on the radio link and it is important sub-carriers. to realize from the start that the characteristics of the radio D = deviation ratio of a frequency-modulated radio link are a central factor in the telemeter design. link. As in any other engineering problem, the choice of E = information efficiency of modulation multiplex methods of modulation, multiplexing, and instrumenta- method. tion to be used in a particular type of telemetry problem F = number of samples per second per channel of a usually depends on a number of practical considerations. time division multiplex. Among these are antenna requirements and limitations, x = information frequency in an individual channel operating conditions, type of instruments used to con- of a multiplex. vert the quantities to be metered into electrical signals for use in modulation, precision required, number of # The symbol D is also used in Section VIII, when discussing quantities to be simultaneously metered and their fre- overmodulation, to denote the overload value.

RADIO TELEMETRY 3 Fc =video pass band of a radio link. Ri = ratio of the carrier improvement threshold to fD = maximum frequency deviation of a frequency- the ith sub-carrier improvement threshold modulated (or phase-modulated) radio car- (the latter expressed in terms of correspondrier. ing carrier strength). fdh = maximum frequency deviation of the highest S = RMS amplitude of the sinusoidal video output frequency sub-carrier. of the comparison single channel AM link fdi = maximum frequency deviation of ith frequency under condition of full modulation. modulated sub-carrier. St = improvement threshold of a frequency- or fh = unmodulated frequency of the highest fre- phase-modulated radio carrier. (Measured at quency sub-carrier. the video output of the fully modulated fi = unmodulated frequency of ith sub-carrier. comparison AM link). FM = frequency modulation. W1 =band width before modulation and after defm =maximum information frequency in a channel modulation. of a multiplex. W2 =band width after modulation and before defmi =maximum information frequency transmitted modulation. in ith channel. FR = cut-off frequency of a recorder. III. Frequency Division Multiplexing in Radio g = fraction of the time between channels in PPM Telemetry or PWM allowed for guard space to prevent overlapping of pulses. overlapping of pulses. It is usually not practical to use a separate radio link k = PAM: video band width in units of nF. for each channel if more than one channel of information k = PAM video band width in units of nF. s t be m sl Two importation K2 = a constant characteristic of the modulation of to be metered simltaneously. Two important reasons the radio carrier. for this are antenna complications and the saving of k2 = RMS fluctuation noise per unit band width in space, weight, and power which usually can be realized the video output of the comparison single by multiplexing onto a single radio carrier. channel AM link. There are two general methods of multiplexing in use. K1 = a constant characteristic of the type of modula- One is frequency division (sub-carriers) and the other is tion of the ith sub-carrier. time division (commutation). A frequency division sysm =an integer. tem uses a separate sub-carrier for each channel with M =i modulation index of the ith sub-carrier. spaced sub-carrier frequencies. The sub-carriers are Mu =modulation index of the radio link due to the mixed linearly and then modulate the carrier. At the ith sub-carrier. receiving end, the sub-carriers are selected out by a N = number of binary digits in a PCM system. linear frequency selective circuit and demodulated. A n =number of channels in a multiplex. time division system samples the information in the PCM = pulse codemodulation. channels in cyclic serial sequence and puts out a pulse PAM =pulse amplitude modulation. (or pulses) for each channel which is modulated in acPM =phase modulation. cordance with the information in each channel. These pn =probability density function for sum of n sub- pulses are then used to modulate the carrier. The carriers, sampling process is usually accomplished by some form P = probability of the instantaneous sum of n of commutator either electronic or mechanical. In some sinusoidal sub-carrier voltages exceeding the cases of slow commutation, the output of the radio revoltage S which will fully modulate the radio ceiver is simply recorded by a pen recorder or on a link. photographic paper and the channels sorted out by inPPM = pulse position modulation. spection. It is also possible to use an automatic appaPWM= pulse width modulation. ratus to sort out the channels from the record, demodu D =maximum phase deviation of a phase-modu- late them, and record them. When a large number of lated radio carrier. channels is sampled at a high rate, a synchronized r =number of side band pairs in the video pass commutator at the receiver is usually provided. band of a PAM multiplex (i.e., video band In specifying the method of multiplexing and modulawidth in units of F). tion used in a system it is customary to work from the R1 =signal-to-noise ratio before modulation and individual input channels toward the carrier.(L2) For after demodulation. example, AM-FM means a frequency division multiplex Ri* =R1 at improvement threshold. with sub-carriers amplitude modulated in accordance R2 = signal-to-noise ratio after modulation and be- with the information in each channel and with the subfore demodulation. carriers frequency modulating the carrier; PPM-AM R* =R2 at improvement threshold. means a time division multiplex with pulses position Roi =wide band improvement referred to the ith modulated (in time) in accordance with the information channel of a multiplex. in each channel and with the pulses amplitude modu

4 M. H. NICHOLS AND L. L. RAUCH lating the carrier; PAM-FM-FM means that a separate emphasized that the cross modulation frequencies occur time division multiplex with amplitude modulated with amplitudes higher than the corresponding harpulses is used to modulate the frequency of the sub- monic. For example, in the case of third harmonic discarriers of a frequency division multiplex the output of tortion, the cross modulation frequencies of the form which frequency modulates the carrier. Thus the last fp-fq4fr, when p q#r, occur with amplitudes six group of letters specifies the modulation on the carrier; times the third harmonic if the amplitudes of all subthe preceding groups of letters specify the type of carriers are considered equal.(ss) Also, as pointed out by multiplex and modulation of each stage. All three letter Stedman,(s5) another effect of third harmonic cross groups start with a "P" which means time division modulation is to increase the amplitude of the fundamultiplex and all two letter groups which precede the mental of each sub-carrier by an amount depending on final group mean frequency division in the multiplex the amplitude of the other channels and the degree of stage corresponding to the position of the group. third harmonic distortion. This effect is important in The method of frequency division has had wide use in AM sub-carriers but not in FM sub-carriers because of telephony particularly over wire links.(C2) Its use in the limiting before demodulation. This effect can be radio telemetry is largely restricted to systems having larger than other third harmonic cross modulation not more than about ten channels. The principal reason effects especially if more than a few sub-carriers are for this is crosstalk which results primarily from non- used, and, of course cannot be eliminated by choice of linearity in the radio link. In principle, crosstalk can be sub-carrier frequencies. Stedman(s6) has shown that this corrected for if the characteristics of the radio link and effect can be used as a convenient method of measuring the phases and amplitudes of the sub-carriers are known the amount of cross modulation in a frequency division at all times. However, this is obviously impractical system using AM sub-carriers. especially when there are more than a few sub-carriers. In the case of more than a few channels, it becomes a Because of the precision required in the metering, it is practical impossibility to eliminate, by choice of subgenerally necessary to suppress crosstalk to 40 db or carrier frequencies, the large cross modulation terms in a more. In frequency division telemetry some form of CW reasonable video band width. In this case the choice of radio transmission is usually used inasmuch as pulse sub-carrier frequencies should depend on other factors methods are better adapted to time division multi- such as noise characteristics of the system (see Section plexing. Due to the particular limitations on operating III-2) and a radio link which is sufficiently linear must conditions imposed on radio links for telemetry, as be procured. already noted, it is difficult to achieve a high degree of In radio links, as well as in other circuits using vacuum linearity in the radio link. In current telemetry practice, tubes, nonlinear effects generally increase as the moduthe better radio links have the order of one percent total lation level is increased. Therefore, there is a certain harmonic distortion in terms of voltage-i.e., of the modulation level (generally called full modulation) order of 0.01 percent of the video power appears in the which, if exceeded, will result in objectionable crosstalk. harmonics when the link is modulated to a reasonable Exceeding this level is usually called overmodulation. In level by a single sinusoidal frequency.t When such a link order to reduce fluctuation and impulse noise effects, it is used to transmit sub-carriers, objectionable crosstalk is desirable to operate the radio link as near full modulacan result particularly when more than a few sub- tion as possible. This is discussed in the next section. carriers are used. 111-2. NOISE CHARACTERISTICS OF FREQUENCY III-1. CROSSTALK IN FREQUENCY DIVISION DIVISION SYSTEMS Frequency division crosstalk has been discussed by In addition to harmonic distortion, discussed in the Bennett(Bl) and others in relation to telephony and by previous section, the radio link introduces noise into the Stedman(s6) in relation to radio telemetry. If there is system. In the interests of maintaining high precision in appreciable harmonic distortion in the radio link and if the metering, it is desirable to keep the individual as many as ten or more sub-carriers are used, the im- channel signal-to-noise ratios as high as possible. In portant cross modulation frequencies number in the comparing noise characteristics (other than crosstalk) of thousands for third harmonic distortion alone.(s5) Thus various types of multiplexing, it is convenient to define when many sub-carriers are used, crosstalk tends toward a wide band improvement ratio, Ro, in such a way that the characteristics of fluctuation noise. it is independent of the carrier signal-to-noise ratio in If there are only a few sub-carriers it is frequently the radio link.(L2) The wide band improvement ratio, possible to choose sub-carrier frequencies so as to elimi- Ro, is therefore defined as the ratio of the signal-to-noise nate in the receiver frequency selector a large portion of ratio of a fully modulated single channel of the multiplex the important cross modulation frequencies-i.e., the system to the signal-to-noise ratio of a fully modulated ones that occur with large amplitude. It should be one channel system in which the information in the single channel directly amplitude modulates a single t For an example of the effort required to reduce radio link channel d i a ude a distortion to a low value see Burrows and Deceno, Proc. Inst. channel radio link operating under the same conditions Radio Engrs. 33, 84 (1945). of received carrier power (as is customary the side band

RADIO TELEMETRY 5 power is neglected in the comparison radio link) and TABLE I. Frequency division noise characteristics. noise power per unit band width. When computing such things as improvement thresholds, it is convenient to First First Second ub-carrier i modu- modu- modu- Sub-carrier improveexpress the radiofrequency noise per unit band width, lation lation lation improvement ment constant index index threshold threshold carrier signal strength, etc., in terms of the output of this single channel AM comparison link. To simplify the Type Ki M,, M2, at/k2 St/k expressions, the full modulation RMS video output, S, AM-AM 1 aoi/S 1 of the radio link carrying the multiplexed signal is taken to be equal to the full modulation RMS video output, S, aoi fdi FM-AM V31 4.6 (fdi) of the comparison link. S fmi At present, most radio telemetry links are operated at VHF or higher. The principal type of noise encountered AM-FM 1 ao/S f 3(f at these frequencies is fluctuation noise. T The analysis in f this paper is for fluctuation noise only and, unless modified, the term "noise" will mean fluctuation noise. FM-FM V3 4.6-(fdi) 3.2(fD) Fluctuation noise has a constant RMS amplitude versus S fmi fi f) frequency spectrum over the range of the RF pass band AM-PM 1 ai/S D 3.2f) of a radio receiver, but the phase distribution is random. However, the RMS amplitude of the noise-frequency aoi fdi 4.6 spectrum of the output of a radio receiver varies with FM-PM v S D (fdi 3.2(fD)* frequency in a manner which depends on the type of'D modulation used, although the phase distribution remains random. This results in two important charac- of the radio link due to the ith sub-carrierl and K2 is a teristics of the final noise output. For any type of noise constant equal to 1/v2.1 with a continuous spectrum, the noise power in a fre- For convenience in the following discussions, Table I quency band of small width Aco is proportional to AW.(LI) gives the values of Ki, Mij, and M2i for the types of Thus the RMS noise voltage is proportional to (Aw)t. modulation used in frequency division telemetry.#* Due to the random phase distribution of fluctuation Since in FM and PM, the noise improvement is not noise, the crest voltage (height of the larger peaks)~ realized unless the improvement threshold is exceeded, is proportional to the RMS voltage, and therefore to the sub-carrier and carrier improvement thresholds are (Ao)i. This is not true in the case of impulse noise, where also given. The nomenclature in the table is defined in the height of the pulse is proportional to Aw.(LI) Section II. In Table I it is considered that the FM and For convenience in setting up Table I which summa- PM improvement threshold of the carrier is reached rizes the fluctuation noise characteristics for frequency when the amplitude of the unmodulated RF signal division multiplexing, Roi (the wide band improvement, equals the crest fluctuation noise in the RF pass band. Ro, for the ith channel) can be written For this determination, a fluctuation noise crest factor of 4 is used(C4 L1) and the RF pass band is taken as Roi= KliMIiM2K2, (III-1) 2.6fo for FM and PM where fD is the maximum freo quency deviation.c(K1 The RMS noise per unit band where Ki is a constant characteristic of the type of quency deviation.(K The RMS noise per unit band i iotn s carrer the i width in the RF pass band is k2/V2 inasmuch as k2 is modulation of the ith sub-carrier, Mi is the modulation.modulation of. u-arei is th mdefined as the RMS noise per unit band width in the index of the ith sub-carrier, M2i is the modulation index v o ** Th video output of the one channel AM system.** The RF improvement threshold is therefore given by t The other type, namely impulse noise, is either man-made or the result of atmospheric disturbances and will not be discussed V2S= 4(2/V2) (2.6fD)). (111-2) in this section. In frequency modulation receivers the wide band improvement for impulse noise is twice the deviation ratio as compared to vJ times the deviation ratio for fluctuation noise. 11 For a discussion of FM and PM modulation indices, noise (See reference C4.) The improvement threshold for impulse noise improvement, etc., see references (C4, H6). is somewhat higher than that for fluctuation noise. (See refer- ~ The value K2= 1,/2 results from the appearance of the subence C4.) carrier and both side bands in the video. Thus with AM sub~ For a rigorous definition of crest-noise voltage, some distribu- carriers, for example, the video band width taken up by the ith tion function must be assumed for the instantaneous noise voltage. sub-carrier is 2fi, wheref,i= maximum information frequency in Many writers, for good reason, assume the normal law as a basis the ith sub-carrier whereas in the comparison single channel AM for theoretical investigations. This law offers a finite probability system the required video band width is fi. The ratio of the square for arbitrarily high noise voltages, but in practice nonlinear circuit roots of the band widths gives the factor K2= 1/V. This value also elements bring the cumulative distribution function to unity for holds for FM and PM. finite values of the instantaneous noise voltage. If we assume the **## In order to simplify calculations in the case of an FM carrier crest voltage is attained when the instantaneous voltage is greater (triangular noise spectrum), the noise amplitude is assumed to be than or equal to four times the RMS value, the normal law pro- constant over the pass band of a sub-carrier and is taken to be vides the result that during a sufficiently long period the crest equal to the noise amplitude corresponding to the center of the value will be reached a fraction of the time equal to 63 X 10". More pass band. Since the sub-carrier pass bands are narrow relative can be said if the amplitude versus frequency distribution of the to their center frequencies this is a good approximation. noise is taken into account. ** See reference (G2), page 249.

6 M. H. NICHOLS AND L. L. RAUCH Where S= RMS amplitude of the sinusoidal video out- advantage is gained unless 10 or more sub-carriers are put of the comparison single channel AM link under used but that there is considerable advantage in allowing condition of full modulation; (assuming peak detection for Pn values even as small as 10-4 when the number of of modulated envelope) the corresponding RMS value sub-carriers becomes large. It is of importance to notice of the carrier signal is therefore S. The relation for the that the value of D is not greatly affected by the value sub-carriers contains k2 instead of k2/V and is given by chosen for Pn provided Pn<<1. In practice, this means Va-=4k2(2.6fT)i. I that if the amplitudes of all sub-carriers are increased V-2ait = 4k2(2.6fdi> (III-3) simultaneously the overmodulation will be negligible III-3. OVERMODULATION VERSUS NOISE until a critical region is reached, after which any appreciable increase of the amplitudes of the sub-carriers As pointed out in Section VIII-1, overmodulation will result in a large increase in the fraction of the time causes undesirable crosstalk. On the other hand, Table I during which overmodulation occurs. shows that for highest signal-to-noise ratio, the sub- In order to operate a frequency division telemeter at carrier amplitudes a0i should be as large as possible. If optimum precision, it is therefore necessary to comprothere is to be no overmodulation at any time, the mise on the fraction of time of overmodulation so that instantaneous sum of the peak amplitudes of the sub- the sub-carrier amplitudes may be increased. There is carriers must never exceed the voltage necessary to fully no point in being so rigorous in the overmodulation remodulate the radio link. Assuming that the distortion is quirement that the signal-to-noise ratio becomes disnot too high, this relation can be expressed in terms of proportionately small-i.e., that the ratio aol/S in the video output voltage as follows: Table I, Column 2, is disproportionately small. n For purposes of discussion, it is convenient to define ami = S, (111-4) the quantity A as the ratio of the sub-carrier amplitude it^~=l~~ ~which will cause overmodulation Pn of the time to the where ami is the fully modulated amplitude of the ith largest sub-carrier amplitude which will cause no sub-carrier and S is the amplitude of the sinusoidal overmodulation at all, assuming all sub-carriers to have video output of the receiver under condition of full the same amplitude. Figure 4 is a plot of A versus n. modulation (and is taken to be equal to the video output For larger vaues of n a very good approximation is S of the comparison single channel AM link). If the A,= 0.43(n)l. In terms of An, the first modulation index unmodulated amplitudes aoi of all sub-carriers are equal Mu becomes to a0, and if all channels are fully amplitude modulated An An fdi -i.e., ai=2a0 —then the maximum unmodulated Mli(AM)=-; Mli(FM)=. (III-7) amplitude ao is given by 2n n fmi ao=S/2n. (111-5) If An= 0.43 (n), then the first modulation index becomes For frequency modulated sub-carriers, the amplitude is Ml (AM) Mi(FM). (43 -8 TMli(-AM) = Mii(FM)=~. (III-8) independent of modulation so Eq. (III-5) becomes for (n)1 (n)I fmi this case a=S/ (I-6) The above results apply to the case of n sinusoidal sub-carriers of constant amplitude but random phase. On the other hand, if overmodulation can be tolerated The application of the results to AM sub-carriers is even a very small fraction of time, considerably larger somewhat different than the application to FM subamplitudes than given by (111-4) can be used if the carriers. For in the FM case, the amplitude remains number of channels is the order of ten or greater and essentially constant independent of modulation so the provided that the phases of the sub-carriers are random. above results are independent of modulation and permit This last condition is satisfied if separate sub-carrier the determination of the maximum sub-carrier amplioscillators are used. The probability, Pn= 1-Cn, of the tude once Pn is chosen. instantaneous sum of n sinusoidal sub-carrier voltages In AM sub-carriers, the above results apply directly exceeding the level S=D for full modulation is calcu- to the case of full modulation simultaneously applied to lated in Section VIII. The results are summarized in all channels. If the full AM modulation capability of the Fig. 3 in which the permissible overload value D is sub-carrier is used, then the use of the curves gives twice plotted versus n, the number of sub-carriers for various the unmodulated amplitude. For a given Pn value, the values of Pn for the case of n sub-carriers all of ampli- condition of all channels simultaneously fully modulated tude (2/n)l (this gives total RMS value unity). The line is the most stringent condition because in general all D= (2n) represents the condition for no overmodula- channels will not be fully modulated at once. In order to tion at any time. The probability Pn may be interpreted take this into account, an additional statistical analysis as the fraction of the time that the overload level for full of the data in the channels would have to be made. In modulation is exceeded. From Fig. 3 it can be seen that this connection, it is sometimes possible, by such things even if values of Pn as large 10-2 are permitted, no great as simply reversing the sign of the data before modula

RADIO TELEMETRY 7 tion, to avoid simultaneous high level modulation on all crosstalk and noise improvement. If the link is AM, then or most of the channels. An example might be adjacent the noise characteristic is rectangular and the net imstrain gauge stations on structural elements. Stedman(S5) provement which can be realized is the usual FM subhas estimated that upon sufficient operating experience, carrier improvement regardless of the sub-carrier freit may be possible to increase the sub-carrier levels by as quency. The relative noise characteristic of the AM and much as a factor of 1.5 to 2 above the levels calculated FM sub-carriers can be readily calculated from Tables by use of Fig. 3. I and II. If in FM-FM, the sub-carrier deviation ratios are 111-4. EFFECT OF MULTIPA TH TRANSMISSION proportional to the sub-carrier frequency and if all subMultipath transmission can lead to serious distortion carriers have the same amplitude, then the individual in the case of an FM carrier(C3GL, M4) and in the case of Roi of all the channels will be the same because of the a fully or nearly fully modulated AM carrier.(Gl) In a triangular noise spectrum of the FM radio link. For the frequency-division multiplex this results in crosstalk. same reason, in AM-FM it is necessary to make each Aside from certain precautions in the design and opera- sub-carrier amplitude proportional to its frequency (pretion of the radio link which are discussed in the above emphasis) in order to have equal Roi for all channels. If references, the multipath effect in radio telemetry can be in FM-AM and FM-PM the sub-carrier deviation ratio reduced by the use of directional receiving antennas is proportional to sub-carrier frequency, then it is provided the transmitter is at sufficiently high elevation necessary to make each sub-carrier amplitude inversely angle above the horizon. By the use of several receiving proportional to the sub-carrier frequency in order to stations distributed along the trajectory, the angle of have equal Roi for all channels, etc. elevation of the transmitter relative to one or more of In addition to noise and crosstalk improvement, when the receiving stations can usually be kept rather high. they can be realized, FM sub-carriers also have the advantage of an output level independent of the output 111-5. SUB-CARRIER MODULATION level of the carrier provided that the individual channel If a reasonably large deviation ratio can be obtained, levels are sufficiently high and provided that effective frequency modulated sub-carriers have the advantage of limiters are used. Thus when an AM carrier is used, for noise suppression which, of course, includes crosstalk example, only mildly effective automatic volume consuppression. Melton(M2) and Coe(Cl) have described FM trol, if any, is required. Another advantage of FM subsub-carrier systems in which the sub-carriers, when fully carriers with large deviation ratio is that the requiremodulated, are deviated -7.5 percent of center fre- ments on the frequency selector to avoid interchannel quency with satisfactory linearity of response and crosstalk are not as rigid-i.e., the attenuation at the compactness of equipment at the transmitting end. neighboring frequencies need not be as great as for AM Thus with a deviation ratio of five, for example, the sub-carriers. maximum information frequency in each channel should As discussed in Section VI, certain types of instrunot be greater than about two percent of the sub-carrier mentation are better adapted for AM sub-carriers than frequency. Therefore, high information frequencies for FM sub-carriers and conversely. Therefore, it is not imply high FM sub-carrier frequencies. If an FM carrier always practical to use FM sub-carriers even if the noise is used, the typical triangular noise spectrum must be and cross talk improvement could be realized because of taken into account. For the noise reduction of the FM added complexity and instability, especially at the sub-carrier is proportional to the deviation ratio but it transmitter end. If the channel contains information follows from above that the sub-carrier frequency and which has essentially DC components, then the FM hence the noise in the sub-carrier pass band (because of sub-carrier frequency must be sufficiently stabilized. On the triangular noise spectrum of the FM carrier) are the other hand, amplitude stability of the FM subproportional to the sub-carrier deviation ratio. Thus, in carrier is only of secondary importance. In the case of this case there is no net increased noise improvement AM sub-carriers, the amplitude must be stabilized but realized by increasing the sub-carrier deviation ratio if a the frequency is of secondary importance so long as the corresponding increase in sub-carrier frequency is re- sub-carrier with its sidebands does not drift out of the quired. However, there is crosstalk improvement pro- pass band of the frequency selector. vided, of course, that the nonlinear distortion of the Phase-modulated sub-carriers are generally not used radio link does not increase in proportion to the video in radio telemetry because in most applications DC refrequency which is often the case, particularly, if the sponse is required. In order to handle DC with phaseFM link operates at a low deviation ratio.(4) On the modulated sub-carriers, additional channels would be other hand, if the maximum information frequency is required in order to provide a time base for detection of low, the frequency selector (sub-carrier filter) often constant phase shift. places a lower limit on the sub-carrier band width so that a high deviation ratio is available without the -6. CHOICE OF SUB-CARRIER FREQUENCIES necessity of running up the sub-carrier frequency. In Although this topic has been touched on in the previthis case there can be considerable advantage in ous sections, it is of sufficient importance to be sum

8 M. H. NICHOLS AND L. L. RAUCH marized here. In the case of more than several AM sub- 111-8. IMPROVEMENT THRESHOLDS carriers on an FM carrier, Stedman(S5) has shown that The sub-carrier and carrier thresholds are given in.,. ~.',,. The sub-carrier and carrier thresholds are given in in the interest of noise improvement the frequencies Table I. In the case of FM-FM or FM-PM the carrier should be spaced as closely at the low end of the video and sub-carriers each have improvement thresholds and band as the frequency selectors will permit. This follows as the carrier signal strength diminishes, one or the other from TlIeuo iteemaas the carrier signal strength diminishes, one or the other from Table because of thefinthedenoinatorof. thresholds will be reached first depending upon the If AM-AM is used, only considerations of instrumenta- parameters involved. If FM-FM is used it follows from tion, cabling to the instruments, restrictions on the radio Table I that the ratio of the two corresponding Table I that the ratio Rti of the two corresponding link band width, etc., need to be taken into account. For carrier strengths is FM-AM it is desirable to realize as large a sub-carrier deviation ratio as possible subject to limitations set /fD\fDaoi down in the previous sentence. In the case of FM-FM, R, =0.71 f. (III-9) crosstalk improvement can be obtained, if the radio link fdi fi S distortion does not increase appreciably with modulating Therefore, if Rti> for all i sub-carriers than the carrier frequency, by increasing the sub-carrier deviation ratio threshold is the determining factor. If all sub-carrier which implies increasing the sub-carrier frequencies. amplitudes are equal and the A, of Section VIII is used, However, no net noise improvement is realized by Eq. (111-9) becomes for the highest sub-carrier freincreasing the deviation ratio if it is necessary to increase qncy fh the sub-carrier frequencies in proportion because of the Rth =0. 7DAn/ (Dfdh) (III-10) triangular noise spectrum of the FM carrier (see Section 111-5). It should always be borne in mind that, with an where D= carrier deviation ratio=fD/fh and fdh is the FM link, increasing the sub-carrier frequencies, keeping frequency deviation of the highest frequency sub-carrier. the carrier deviation ratio constant, increases the carrier Thus there is a lower limit on D above which the carrier improvement threshold. In the case of a PM carrier, the threshold governs the system. In a similar way it follows height of the rectangular noise spectrum is independent from Table I that for FM-PM of the carrier video band width if the phase deviation is R= 0.71nDA /nf /fdi ) (-11) held constant. Therefore, in this respect, a PM link is like an AM link except that the PM link has an im- IV. Time Division in Radio Telemetry provement threshold which, if the phase deviation is constant, increases in proportion to the square root of Generally speaking, the problem of crosstalk in many the video band width (see Table I). channel radio telemetry is handled with greater ease by time division than by frequency division. The reason 111-7. CARRIER MODULATION for this is that in the radio link it is usually easier to Provided that the received carrier signal is sufficiently obtain suffcient band width to keep the time division strong to exceed the improvement threshold, the noise crosstalk down than it is to obtain sufficient linearity to improvement in FM and PM radio links, which can be keep the frequency division crosstalk down particularly realized with sufficient frequency or phase deviation, is when a large number of channels is required. Numerous of importance in increasing the precision of the metering. types of pulse modulation can be used after the synthesis Also, the video output level of an FM or PM receiver is after the cyclic sampling of the channels). Three essentially independent of the received signal strength types in use in telemetry are pulse amplitude modulaas long as the limiting threshold is exceeded. There are tion, pulse wdth modulation, and pulse position modualso practical considerations, particularly at the trans- laton. Pulse code modulation is currently being conmitter end which influence the choice of carrier modula- idre ae of its erently large signal-to-noise ratio and the convenience with which it can be tion. In current practice, most of the frequency division r systems use an FM radio link. Possibly one of the relayed reasons for the use of FM radio links in small units is IV-1. FREQUENCY RESPONSE OF TIME DIVISION that the carrier modulation can be applied at low levels and easily amplified without too much distortion. For In time division each channel is sampled in sequence at a repetition rate F. The information is carried by small AM units it seems to be most practical to perform reeo rate F. Te information is carried by some form of pulse modulation. The purpose of this the modulation at high level which leads to larger, the modulation at high level which leads to larger, section is to set down the individual channel frequency heavier components and to more distortion unless suffi- r response in terms of F. For this purpose, it is convenient cient feed back is used. to consider two types of modulation, pulse amplitude In deciding which type of modulation to use it must and pulse width, inasmuch as the other types are realways be borne in mind that unless sufficiently strong duced to one of these in the process of recovering the carrier signals are received-i.e., unless the improve- original channel information from the pulse modulation. ment threshold is exceeded-FM and PM are worse In this discussion, it is assumed that at the receiver the than AM as far as noise is concerned. pulses are sorted out according to channel so that the

R A DIO TELEMET R Y 9. —.', < _maximum frequency response of F/2. In practice, the n/-~ l^~ maximum frequency is somewhat lower because of the - ^ -.... - ~ impossibility of making vertical cut-off filters. A con_I I I ventional low pass filter which transmits with negligible TIME - distortion up to 0.4F and is cut off sufficiently by 0.6F is FIG. 1. Schematic wave form of pulse amplitude modulation. The feasible provided F is not too small (see Section IV-4.4). dashed curve represents the wave form before sampling. Such a filter results in a maximum undistorted frequency response of 0.4F. It is important to note that if at the information in each channel is carried by a series of transmitter end a channel information frequency of modulated pulses. This sorting out may be done by rter n. nee it will prouce distortion greater than 0.4F is inserted, it will produce distortion a synchronized commutator or by other automatic at thereceiverbecause termsofthetype mF-<0.6F methods or it may be done "by hand by inspection of methods or it may be done "by hand" by inspection of where m is an integer, will pass through the filter. If the recorded pulses of several or all channels on the same components higher than 0.4F are possible, then a low channel of a recorder. It is assumed in each case that theF are p, tn a pass filter must be inserted in the channel at the transsampling of each channel occurs at evenly spaced intervals. sampling is done at unevenly spaced, mitter ahead of the commutator which performs the intervals. If the sampling is done at unevenly spaced sampling intervals(H2) the frequency response is less than the corresponding evenly spaced case. The analysis in the IV-1.3. The Pulse Widener with Pulse unevenly spaced case is difficult to carry out and no Amplitude Modulation attempt is made in this paper to develop this problem inasmuch as it is about equally feasible to perform the If the pulses of Fig. 1 are widened before they are fed sampling at evenly spaced intervals.(M3 R3) to the recording galvanometer the peak galvanometer current required is considerably lower than in the case IV-1.1. Direct Recording of Pulse Amplitude Modulation of direct pulse recording. If the information is sampled The wave form after sorting out is shown sche- at the transmitter end during a length of time small matically in Fig. 1. In some radio telemetry systems in compared to 1/F-as is the case if a large number of use, this wave form is recorded directly. Let the fre- channels are used-the height of the widened pulse is quency response of the recorder be such that the heights essentially the instantaneous value of the information at of the individual pulses recorded are not influenced by h sampling. In practice the pulse in the eth channel is widened until the pi- 1th channel in the next the height of any of the other pulses. The usual pro- (t a i te ne cedure in handling such a record is to draw a smooth commutator sequence is turned on at which time the curve through the peaks of the pulses. It has been pulse widener of th channel is discharged to zero and is estimated that if reasonable care is used in smoothing then ready to widen the next pulse in this channel.(K3) "by eye," at least five to six samples per cycle of Thus in the case of a large number of channels, the pulse information are required in order to keep the uncer- is widened to essentially the maximum amount. tainties less than about five percent. If the recording galvanometer has sufficient frequency tainties less than about five percent.h e If the individual samples are short in duration, the response to essentially reproduce the rectangular shaped recording of the output pulses directly by recording pulses, then pulse widening is of no particular advantage galvanometers becomes difficult because of the large except possibly to reduce the writing speed of the pulses of current required. Sometimes cathode-ray recorder. The advantage of pulse widening as far as recording is used in which case the voltage pulses can be reducing the required galvanometer current comes from recorded directly. However, as will be seen in Section the use of lower frequency recording galvanometer IV-4, any channel output pass band greater than the elements in connection with the widened pulse. information band which can be realized from each At this point there are essentially two ways of handling channel-i.e., greater than about F/6 in this case- the widened pulses (1) Use a recording galvanometer of reduces the signal-to-noise ratio. lower frequency response than is required to reproduce the sharp corners of the widened pulse but with suffiIV-1.2. The Low Pass Filter with Pulse cient frequency response to record the flat top near the Amplitude Modulation middle of the widened pulse independently of the height It can be shown by Fourier analysis(B2) that the frequency spectrum of a pulse amplitude modulated channel with sinusoidal information of frequency f is as indicated in Fig. 2. The spectrum consists of a series of I side band pairs several of which are shown. The original F-f F-f 2F input can be obtained without distortion by inserting an FREQUENCY ideal low pass filter which cuts off at F/2 or by an ideal band pass filter which passes the band mFF/2 where FIGro. 2. Frequency spectrum of pulse amplitude modulation in which a sinusoid of frequency f is sampled F times per second. m is an integer. It is clear that such filters would permit a Several side band pairs are included.

10 M. H. NICHOLS AND L. L. RAUCH TABLE II. Fluctuation noise characteristics of time present this may be of considerable practical advantage. division telemetry. division telemetry. With suitable compensation and with an ideal low pass RMS carrier filter of cutoff at F/2, the frequency response is the same threshold as that of method (IV-1.2) namely, O f<F/2. Type Roi St/k2 Reference I a IV-1.4. Pulse Width Modulation PAM-AM (R4) The type of pulse width modulation most frequently 7AfD b met in radio telemetry is that in which one edge of the PAM-FM 3.2(f0D) (R4) anF(r)i pulse is fixed in the time sequence and the other edge 1~ /~F \~ c,"' d varies in accordance with the information; the width of PWM-AM 1[~/~ 4 ( ApFc pend PWM-AM n\) 4(F,) G Appendix 1 the pulse is proportional to the instantaneous value of the information at the time the variable edge of the PWM-FM ~D(c) 3.2(D) c Appendix 1 pulse occurs. In PWM-AM, the transmitter is turned on full power during the pulses and turned off in between. 5Fe d In PWM-FM the transmitter is fully modulated in the PPMAM 4n0F 4(2nF)4 Appendix 2 positive direction during the pulses and fully modulated PCM-AM (See Section JV-5) 4(nNF)i Appendix 3 in the negative direction between the pulses, or vice PCM-AM (See Section IV-5) 4(nNF)t Appendix 3 versa. In each case the width of the pulses is modulated in accordance with the information. If at this point, the It should be noted that in each case Fe refers to the video band width used in accordance with the information. If at this point, the in that case. pulse width modulation is converted into pulse ampliThis is an approximate expression which holds to better than eight percent if an >20 and r/an>5/4. tude modulation with samples equally spaced, then the b This is an approximate expression which holds to better than 10 percent if ane20 and r/anl1. results of PAM apply. The other alternative is to pass * Assumes an average duty cycle of 0.5. d These results are based on the assumption that there is an essentially the width modulated pulses through a low pass filter. noise free time reference for each channel. If the channel reference in PWM This has been discussed by Kretzmer.(K5) In this case is obtained by the beginning of the pulse, the Roi above must be divided by b ree V2. If the channel reference in PPM is obtained by a second pulse in each frequency components of the type mFi-nf, where m channel, then the Roi above must be divided by 2 (not by V because of the en ne, er doubling of the duty cycle). and n are integers, are generated whereas in pulse e Actually there are two thresholds in this case: the FM carrier threshold and the pulse threshold in the video. It is assumed that the carrier threshold amplitude modulation only frequency components of occurs at a higher signal strength than does the pulse threshold. the type mFf are generated. Thus in the case of pulse amplitude modulation a low pass filter with vertical of the other pulses. After the recording is made a smooth i in i cut off at F/2 can be used with no distortion as long as curve is then drawn through the points at the center of r c no information frequency components greater than F/2 the flat top of each pulse. Then as in Section IV-1.1 at ^ leas*fietsisaplepe cycle of inn are inserted at the transmitting end. However, in pulse least five to six samples per cycle of information are width modulation terms of the type F- nf appear with required and a delay of one-half sampling period is (. finite amplitudes. Kretzmer(KS) has shown that if the introduced into every channel. This introduces the introduced into every channel. This introduces the width modulation in the above case does not exceed five problem of locating the center of the pulses. (2) Use a. *. r a l i percent of the repetition period, terms of the type F- 2f recording galvanometer (or a low pass filter preceeding preenter with about three percent of the input information the galvanometer) which cuts off ideally at F/2 (see a a s o t amplitude and terms of the type F-3f enter with 0.1 Section IV-1.2). This gives no distortion due to com-. Section 1.2). This givs no distion de to co- percent approximately. Thus under these conditions ponents of the type mF-f, when m is an integer but *ponents of the type m-f, when m is an integer but only two samples per cycle of information are required if introduces the "aperture" effect.(B, KI) If the widened several percent distortion can be tolerated. pulses have flat tops then the aperture effect introduces r a lit n o t t (in/ f/F// The above reasoning also applies in many cases to the amplitude distortion of the type B (sin7rlf/F)/(r'f/F).. ^ w r plitd ist th frtion of the max.imum possl w h decoding of pulse position modulation in which the rewhere f is the fraction of the maximum possible width c s 1/F t.o whi. thpsa i. A linear^^ i- i ceived pulses are used to produce pulse width modulation 1/F to which the pulses are widened.(a3) A linear phase ^ deay t wic/ is aulsos inrowduced. If na phase * r. by such means as "flip-flop" circuits.(KS) Kretzmer(K5) delay- TJf/r is also introduced. If no compensation is. iasitc..ocompensation is ^... has also pointed out that "symmetrical" pulse width used, if 3= 1, and if the attenuation is not to exceed five.'''.. i t. -,~ i modulation —i.e., both leading and trailing edges are percent, computation shows that about six samples per modulatd-intro lesdis n than does the ", r-r. ~., /T. 1JI. -1 modulated-introduces less distortion than does the cycle of information are required. (It should be noticed i i o on unsymmetrical type in which only one edge is modulated. again that the method of Section IV-1.2 does not introduce any distortion over the frequency range 0 <f< F/2.) IV-2. CROSSTALK IN TIME DIVISION If the aperture effect is compensated for by the insertion Since in time division only one channel is sampled at of a proper network prior to recording,(sMi then pulse a time, the only possibility for crosstalk (aside from such widening has the advantage of enhancing the informa- things as improper shielding of the individual channels) tion components over the method of Section IV-1.2 by is insufficient band pass in the radio link and other a factor 3noa where n is the number of channels and 1/a common circuits. With a radio link and other common is the fraction of the allotted time, 1/nF, during which circuits having an infinitely high cut-off frequency (and the channel is sampled. If there are DC components also with adequate low frequency response) there would

RADIO TELEMETRY 11 be no crosstalk. Nonlinearity in the radio link and other mum acceptable individual channel signal-to-noise ratio common circuits does not cause crosstalk in time divi- may be expressed in terms of the fully modulated sion but results only in a corresponding nonlinearity of sinusoidal output of RMS amplitude, S, from the response in each individual channel. equivalent AM single channel receiver and in terms of The details of required band width, etc., vary some- the RMS noise k2 per unit band width in the output of what with the type of modulation used and will be this receiver by multiplying 1/Roi by (20/V2)k2(fm), discussed in subsequent sections. where fm is the cut-off frequency of the channel output low pass filter. The second factor is the minimum carrier IV-3. FLUCTUATION NOISE IN TIME signal for the AM single channel reference. Once the DIVISION SYSTEMS minimum signal strength is decided on, it is frequently Table II summarizes the fluctuation noise charac- desirable to adjust the improvement threshold to teristics of the types of time division which are used in coincide with this value. radio telemetry. Because of its unique properties to be The quantities in Table II depend upon the video discussed later, pulse code modulation appears to have band width used in each case. The band-width conpossibilities in telemetry but inasmuch as PCM systems siderations are somewhat different in the different types when above threshold, are essentially unaffected by of modulation and are discussed as follows. fluctuation noise, the Roi for PCM is not included in the R i IV-3.1. Band-Width Requirements in PAM table but quantization noise will be given in Section IV-5. However, the improvement threshold for PCM-AM is In Fig. 2 were plotted a few side band pairs which are given, characteristic of a single channel of a time division Table II lists the wide band improvement Roi of a system using on-off switching. In PAM the signal single channel versus the type of modulation. It is handled by the radio link and other common circuits is assumed that all channels are sampled at evenly spaced the superposition, with the proper phases, of such freintervals and at the same rate, and that the output of quency spectra for all individual channels. If the number each channel is fed through a low pass filter with cut-off of side band pairs transmitted is insufficient-i.e., if F, at fm<F/2. It is also assumed that the carrier threshold is not large enough-crosstalk will result. Crosstalk will is exceeded and that perfect synchronism between also result if the gain of the radio link varies appreciably transmitter and receiver commutators is maintained. In over the pass band (amplitude distortion) or if the phase the formulae for PPM-AM and PCM-AM it assumed characteristic departs appreciably from a linear dependthat the pulses have the shape characteristic of the ence on the frequency (phase distortion). The pass band impulse response of the narrowest band width to which of the radio link must extend at least to the lowest they are subjected.(G2) The threshold signal strengths information frequency in any of the channels. If there is are expressed in terms of St, the RMS amplitude of the appreciable amplitude or phase distortion at the lower sinusoidal video output of the comparison single channel frequencies, crosstalk can take place between channels fully modulated AM link as in Section 111-2. In widely separated in the scanning sequence, whereas PAM-FM and PWM-FM it is considered that the when there is distortion at the high frequencies the threshold has been reached when the amplitude of the crosstalk is between adjacent channels. RF signal equals the crest fluctuation noise in the RF If DC components are present in the individual pass band. In PPM-AM, PWM-AM, and PCM-AM the channels, which is often the case in radio telemetry and threshold signal is considered to be reached when the if on-off switching is used, the radio link must have a pulse amplitude in the video pass band is twice the crest DC response and DC stability. These requirements are fluctuation noise in the video pass band. In the calcula- difficult to comply with and can be avoided by "plustions, a crest factor of 4 is used.(c4 LI) minus" sampling.(B2) For this type of sampling one may The minimum acceptable signal-to-noise ratio in the imagine that the commutator reverses the polarity of individual channels generally does not occur at the the connections on alternate contacts with each indicarrier improvement threshold unless the RF band vidual channel. In practice this has been accomplished width is adjusted to make this happen. The minimum in radio telemetry by using a carrier in each channel acceptable signal-to-noise ratio in the individual channels which is amplitude modulated by the information in depends on the nature of the measurements to be made that channel.(R3) The frequency of the carrier is some and this will usually vary from one experiment to integral multiple or submultiple of the sampling freanother. However, perhaps a reasonable criterion for quency F and is arranged so that the sampling occurs minimum acceptable individual channel signal-to-noise alternately during positive and negative half-cycles. In ratio is that the noise will exceed 10 percent of the fully this case side band pairs occur at F/2, 3F/2, etc., which modulated individual channel signal only five percent of carry the information. The side band pair at F/2 can be the time. On the basis of normally distributed noise, filtered out by an ideal low pass filter which must cut off this requires that the RMS individual channel signal at F or, in order to eliminate DC drift and other very equals 20/~2 times the RMS noise in the channel. The low frequency noise, by a band pass filter which cuts off minimum carrier signal which will produce this mini- at F and at some frequency which is lower than (F/2) -fm

12 M. H. NICHOLS AND L. L. RAUCH where fm is the maximum information frequency. By the only part of the radio signal that carries information this method the effect of DC drift in the radio link and is the modulated edge of the pulse; the transmitter other common circuits is completely eliminated. The power during the flat top of the pulse is therefore wasted. output of the filter is the side band pair about F/2 In PWM-FM, Roi can be increased by increasing the representing amplitude modulation by the information. deviation ratio D but with a corresponding increase in St This is then demodulated in the usual way. Since in this only proportional to (D)*. However, the results still do case the energy for the first side band pair comes from not compare favorably with PPM-AM, for example. the first two terms in the Fourier expansion, the Ro0 ex- Nevertheless, PWM-FM is used in some telemetry pression in Table III for PAM-FM and PAM-AM is applications, presumably because of technical reasons. also the correct expression for the case. The only source of crosstalk, aside from such things as Phase or amplitude distortion at the high frequency improper shielding of individual channels, coupling of end of the pass band causes crosstalk between the individual channels via the power supply, etc., is overadjacent channels. The effect of pass bands with varying lapping of the pulses. This can be avoided by providing high frequency cutoffs is discussed in Section IX. a guard space between pulses. The formulas in Table II Figure 5 gives curves of crosstalk in db between adjacent do not allow for this space. If the guard space is a fracchannels as a function of the high frequency cutoff in tion g of the maximum space for channel, l/nF, then the units of nF assuming no other amplitude or phase Roi for PWM-FM must be multiplied by (1-g). If in distortion in the radio link. This figure shows that the PWM-AM the average power is kept constant, the Roi introduction of "blank" spaces between the channels- must be multiplied by (1-g)i. i.e., when each channel is sampled a fraction 1/a of the It should be noted from Table II that Roi for time l/nF allotted to it-results in better crosstalk PWM-FM contains the deviation ratio D times (Fc). suppression. Some of the curves show definite optimum Under condition of constant RF band width, it would transmission band widths which suggest the possibility at first appear desirable, in order to keep Roi large, to of reducing the required band width by proper shaping make Fc small and D correspondingly large. However, of the attenuation characteristic and choice of sampling the increase in transient decay time would require a periods. This is discussed by Bennett(B2) and others.(B4) large guard space in order to keep the pulses from overFrom Table II, it can be seen that, to within the ap- lapping thus causing crosstalk. The guard space must be proximation noted therein, Roi for PAM-AM is inde- at least 1/Fc seconds(G2 —i.e., 1-g< (FC-nF)/Fc. If pendent of the band width and independent of a as long the equality sign is taken, it turns out that with constant as the average RF power is constant. However, it is RF band width, W2, Roi has a maximum value when usually desirable to limit the band width required to F= 3nF given by keep the crosstalk down by choosing a value of a some- Roi= 0.4W2/nIF. (IV-1) what greater than 1. In the case of PAM-FM, Roi and St must be con- IV3.3. Band-Width Considerations in PPM-AM sidered. Since DF,=fD is limited by radio link design In this case it can be seen from Table II that Roi is considerations and by the magnitude of St desired, it is proportional to the video band width Fc and that St is desirable to keep a(r)i as small as possible, consistent independent of F,. In order to keep Roi large, F, should with sufficient crosstalk suppression, in order to keep be large provided that the transmitted pulses have the Roi large. For example, reference to Fig. 5 shows that if shape characteristic of the impulse response for a band crosstalk is to be kept below 40 db, a= 1.1, and r= 1.5n width of F,. Thus as F, is increased, the peak power is a good choice; if below 50 db, a= 1.4, and r= 3.5n is a must also be increased to keep the average power congood choice; and if below 60 db, a= 2, and r= 3.6n with stant. This in addition to other factors, limits the band the pass band essentially cut off by r=4.5n is a good width because generally larger equipment is required choice. The value a= 2 and r=3.5n will be used in the the larger the peak power. It should be mentioned that numerical illustrations to follow. In order to keep Roi as F, should not be any larger than the effective band large as possible, it is also necessary to keep F as small width to which the pulses are subjected. For example, if as possible. From Section IV-1 it follows that this can a modulated power oscillator is used for transmitting the best be done by a low pass output filter with cut off as pulses at around 300 megacycles, it is difficult to obtain close as possible to F/2. efficient operation with an RF band width greater than about 4 megacycles;(R1) thus in this case the maximum IV-3.2. Band-Width Considerations tn PWM F, is about 2 megacycles. It should also be mentioned Table II shows that in both PWM-AM and PWM-FM that the PPM-AM formulae in Table II do not allow for the wide band improvement R0o is proportional to (F,)i a guard space between channels to prevent overlapping but the threshold, St, is also proportional to (Fc)i. of the pulses. If the guard space is a fraction g of the Therefore improvement in Roi by increasing F, is always maximum total space 1/nF, then the R0o must be accomplished at the expense of an increased threshold. multiplied of (1-g). In order to prevent the pulse from As compared to PPM-AM, for example, this is a very a given channel from encroaching on the guard space it serious objection to PWM and results because in PWM may be necessary to provide limiters in the individual

RADIO TELEMETRY 13 information channels prior to commutation at the PAM-FM is v3D(f/FR). On the other hand, if the synthesizer. It is clear that under these conditions there recorder cut off frequency is low-but sufficiently high is no possibility of crosstalk in a PPM system except to reproduce the decommutated pulses without apprecifrom such things as improper shielding of channels. able overlapping, that is about 4F or greater-the recorder tends to integrate the noise and the results are IV-3.4. Band Width for PCM approximately the same as those of pulse integrationIn this case it is only necessary to provide sufficient see Appendix 4. video band width to keep the individual pulses from Thus, in either case, the signal-to-noise ratios are no overlapping appreciably. If the video band width is better than with the low pass filter. In fact, since roughly taken to be l/, the reciprocal of the pulse length, the six samples per sample of information are required if the required video band width is nNF since nNF pulses per smoothing is done "by eye," whereas in the case of a second must be allowed for. -a low pass filter as few as 2.5 samples per cycle are required with high quality filters, Table II shows that the IV-4. FLUCTUATION NOISE CHARACTERISTICS OF signal-to-noise ratio in the low pass filter case can be SYSTEMS WHICH DO NOT USE THE LOW several times higher than for the case of recording PASS OUTPUT FILTER without filters. without filters. As previously pointed out, the results in Table II are based on the case of a low pass filter in the output of IV-4.2. Recording Pulse Width Modulation and Pulse each channel with cutoff fm<F/2. In numerous teleme- Position Modulation with High Frequency Response ter systems now in use, the low pass filter principle is not The method considered here is to record the pulse plus used with the result of generally poorer fluctuation noise noise directly so that its width or position can be characteristics. Several examples are discussed as subsequently measured. In principle, the width is then ~~~~~follows,~~. ~plotted as a function of time and a smooth curve drawn IV-4.1. Recording Pulse Amplitude Modulation wihthrough the points. In practice, the width of the pulse High Frequency Response may be recorded by intensity modulating a cathode-ray beam so as to give a line whose length is equal to the If the recording is done without decommutation-i.e., length of the pulse plus noise. Pulse position may be if all channels are recorded in natural time sequence on a recorded by intensity modulation which produces a dot single recorder channel-and if a smooth curve is to be when the pulse (plus noise) occurs.tt In this type of drawn through the peak of each pulse of an individual recording the frequency response of the recorder, FR, channel (see Section IV-1.1) then the frequency response should be equal to the video response F,. Then by refermust be sufficient to prevent the height of any pulse ence to Appendix 1 it is easy to show that from depending on the height of any other pulse. In this case the frequency response of the recording instrument for PWM-AM, R0-= (/nF)(FRfm), must extend at least up to about 4nF(G2) in order not to for PWM-FM, Roi= (2vD/nF)(FRfm), have more than about one percent cross talk. If the (IV-2) channels are decommutated and the pulses in each and channel recorded on a separate recorder or channel, (see for PPM-AM, Roi= (5/2V)[FR(fm)'/(nF)]J. Section IV-1.1), and if there are many channels, then in order to have the height of each pulse independent of the Reference to Table II will show that the wide band other pulses the frequency response of the recorder must improvements in the corresponding cases with low pass extend up to at least about 4F if the distortion is to be output filter are better than those of Eq. (IV-2). This is kept within several percent.* The record in this case especially so when it is considered that about 6fm would consist of rather broad pulses through the peaks samples are required without the low pass filter and as of which a smooth curve must be drawn. As stated in low as about 2.5fm with the filter. Section IV-1.1 it is estimated that at least five or six It should be pointed out that PWM or PPM can be samples per cycle of information are required if reason- converted into PAM at the receiver and handled by the able care is exercised in smoothing "by eye." PAM methods discussed above or vice versa. If the recorder frequency, FR, is sufficiently high to essentially reproduce the pulses-i.e., equal to the video IV-4.3. The Effect of Pulse Integration band width, F,, which should be at least about 4nF- Consider the individual channel pulses of Fig. 1. When then the RMS noise on top of the pulses is just the video noise is present, it will be superimposed on top of the noise. In this case it is easy to show that the wide band pulses. Suppose that by using an integrating circuit, improvement Roi for PAM-AM is (oafm/FR)t and for tt If the pulses plus noise are first demodulated, as by a trigger * The value of 4F is arrived at by considering that the channel circuit, and then fed to the recorder still in the form of time pulse is of short duration so that the problem reduces to a 6-function modulation, FR may be somewhat less than FC. In this case the impulse through a low pass filter with cutoff at FR. The well-known corresponding Roi is given by Eqs. (IV-2) with FR replaced by F, response is sin2nFRt/2'FRet. if such effects as width of the recording trace, etc., are neglected.

14 M. H. NICHOLS AND L. L. RAUCH TABLE III. Comparison of systems of Table II with equal to RMS quantization noise ratio for a binary code of N radiofrequency band width.. radiofrequency band width., digits is shown by Bennett(B3) [see Eq. (1.3) of Bennett's Ratio Roi s paper] to be ~ ~ ~ ~- -R - R= (3/2)i2N. (IV-3) PAM-AM 0.8nF PPM-AM F, Thus for a seven digit code, N= 7 and R= 150 regardless of the RF signal strength as long as it is above threshold. PAM FM 0.5 0.5() It should be realized that R applies to full modulation. PPM-AM \nF/ At low modulation, the signal-to-noise ratio may be PCM-AM (N/2)i small. For example, at one-tenth full modulation with PPM-AM N= 7, R= 15 regardless of signal strength. In the other PWM-AM 0nF\ F, \ systems of Table II or Table I, the full modulation PPM-AM Fr J \2 nF)J signal-to-noise ratio can be large for high signal strengths and consequently the signal-to-noise ratio at low channel PWM-FM 0.6b 0.5( modulation levels can also be high. This effect should be PPMM taken into account in the choice of N. In some cases a -~ ~~ -~~~ ~~ ~binary code with N= 10 may be required on this ac* In this table Fc refers to the video band width used for the PPM-AM. r e w may e onts b Equation (IV-1) was used to compute this ratio. count. The quantity R can be made essentially constant independent of modulation level by logarithmic such as a resistance and capacitance in series with quantization. RC>>l/anF, the top of the pulse is averaged during the It is likely that the simplest way to handle PCM at interval of time the pulse is on. It is shown in Appendix 4 the receiver is to convert to PAM and use a low pass that the result is exactly the same as using a low pass filter in the output of each channel. The results of filter with cutoff at F/2. Integration with or without Section IV-1.2 show that the maximum undistorted pulse widening can be applied to high frequency frequency response is F/2. recording with the resultant decrease of noise by the In applications where it is necessary to relay the radio above factor. It should be pointed out here that the use signals from the telemeter transmitter by radio links, of pulse widening does not alter the signal-to-noise ratio PCM has great advantages because it is only necessary since both information and noise components are en- to reshape the pulses and retransmit. This process does hanced by the same amount. not change the noise level because the signal is not If the output of the pulse integrator is recorded with- decoded until the end of the relay chain. With the other out the smoothing action of a low pass filter as individual types of multiplexing, the noise (and also crosstalk in samples, then about 6fk samples per record are required frequency division) is generally increased each time the as compared to as low as 2.5fm in the case of a low pass signal is relayed. In case digital computers are to be used output filter. on received data, there is some advantage in having the individual channel data already in digital code. This IV-4.4. General Considerations form is also convenient in some forms of data storage. The above results indicate that the use of a low pass No papers on pulse code radio telemetry in the filter results in a better signal-to-noise ratio than does unclassified journals have come to the authors' attenhigh frequency recording. The use of a low pass filter tion. Coding tubes have been constructed(52s but they gives a smoothed record which is usually a great con- require a relatively high level input which means that, venience and which requires fewer samples per cycle of with much telemetry instrumentation such as resistance information which in turn usually leads to simpler strain gauges, more stages of amplification are required. equipment. The coding can also be done by coding circuits.(GIBS) At low sampling rates, a low pass filter constructed of To be of practical use in radio telemetry, these circuits passive components with cutoff lower than a few tens of must be sufficiently stable and must also often times cycles per second has been generally impractical to handle DC componentsunlesssuch thingsasplus-minus construct. By the application of new principles one of sampling are used. (See Section IV-3.1.) the authors (LLR) has found that it is practical to con- IV-6. COMPARISON OF FLUCTUATION NOISE CHARACstruct low pass electric filters with relatively sharp cutoff TERISTICS OF THE SYSTEMS IN TABLE II ON at frequencies of several cycles per second or con- THE BASIS OF EQUAL RADIO FREQUENCY siderably less. BAND WIDTH IV-5. PULSE CODE MODULATIJON FOR TELEMETRY Since PCM is essentially independent of fluctuation noise when above improvement threshold, only the Pulse code modulation is essentially independent of threshold will be compared in this case. Inasmuch as fluctuation noise when above threshold.~02) There is, single side band transmission is usually not used in radio however, a quantization noise resulting from the use of a telemetry, the RF band width will be taken as twice the finite number of digits. The RMS full modulation signal video band width F, for PPM-AM and PCM-AM. For

RADIO TELEMETRY 15 PAM-FM, the RF band width is taken as 2.6fD(Ki), IV-7.2. Impulse Noise in PPM a=2, and Fc=3.5nF. For PCM-AM a seven digit ary cde w For cmu te i vemndt Unless discriminated against, strong impulse noise in binary code will be used for computing the improvement... i. threshold (see Section JTV-). For Table III, PPM-AM this case can trigger the circuits just the same as an threshold (see Section IV-5). For Table III, PPM-AM threshod (e S n. Fr T e I, information pulse. If the impulse noise does not interfere is used as a basis of comparison; other ratios can be ob-se does not interfere t.amed aaby lipy oraivdng theapr a ratios c..... ob with the synchronizing, a single noise pulse will generally tained by multiplying or dividing the appropriate ratios affect only one channel. However, if the information given in the table. The same number of channels n, and * T pulses are also used for switching the receiver comthe same sampling rate, F, are used in each case. In each u as s o in l ^ ~1 r.~ * a' T mutator, as is often done,(M3) a single noise impulse can case a low pass output filter with cutoff at fm is used. In i n i e' *~' ~ *~'*'~ r'~ 11 also affect all the following channels in the commutation the radiofrequency region where it is feasible to use all types listed in Table III, Fc is generally larger than nF sequence. */^ ~.1 u ~ TTY ~.^ ^If the receiver commutator sequence is initiated by a by sometimes as much as ten or more. Under this con- ir su i i dition it is clear that PPM-AM and PCM-AM (with master pulse, it is generally feasible to make this pulse. longer than the minimum length characteristic of the sufficiently large N) give better noise performance in g both Ro. P M c s f y as fr as video cut-off frequency Fc or to code the pulse. Howboth Roi and St. PAM-FM compares favorably as far as Ro. is concerned but has a larger St. PWM compares ever, if the average power is left constant, it is not vonrn bt; tha lrgea r ti i.. a t'' compatible with maximum fluctuation noise improveunfavorably in St; the reason for this is that the.. s s *. a ment to make the individual information pulses longer transmitter power is essentially wasted during the flat i i i top portion of the pu. or to code them because this would reduce the pulse top portion of the pulse. height and therefore decrease the signal-to-fluctuation IV-7. IMPULSE NOISE IN TIME noise ratio. This effect is not serious in the case of the DIVISION MULTIPLEXING master pulse since it occurs only once each sequence. It is not the purpose of this paper to discuss in detail Impulse noise considerations in PWM are essentially the effects of impulse noise; however, it has seemed to be the same as in PPM except that it is conceivable that desirable to include some brief remarks on impulse noise some form of pulse width discrimination could be usedat this point. In considering impulse noise it should be i.e., a pulse could be discriminated against if it is shorter born in mind that radio telemetry in flight testing is than the minimum pulse width used in the carrier. generally carried out under special conditions in which it is usually possible to suppress most of the man-made IV.3. Impulse Noise in P impulse noise at least during the flight. Also the testing The effect here of strong impulse noise is similar to is usually carried out during periods of settled weather that in PPM in that a strong impulse can either add or so that atmospheric impulse noise is at a minimum. If subtract an information pulse. the impulse noise cannot be eliminated, its effect can be reduced by various methods of pulse discrimination all IV-8. SOME CONSIDERATIONS INVOLVED' IN THE of which decrease the signal to fluctuation noise by three CHOICE OF TYPE OF CARRIER MODULATION to six db or more. IN TIME DIVISION TELEMETRY IV-7..I Impulse Noise in PAM The choice of type of modulation in any frequency region usually depends upon a compromise among Assuming for the moment that the impulse noise does numerous considerations such as antenna and propanot affect the synchronism of the commutators, it is gation problems, frequency allocations and band widths, clear that a single impulse will in general affect only one required range, power available, space and weight channel and its duration will depend upon the cut-off limitations, minimum acceptable signal-to-noise ratio, frequency of the individual channel low pass filter. If the etc. It is not within the scope of this paper to give a commutators are synchronized by a "master" pulse thorough discussion of this problem but a few brief which occurs in the beginning of each sampling sequence, remarks are included in this section. it is possible to discriminate against impulse noise The video frequency should extend up to about 3.5nF affecting synchronization by such things as making this in PAM in order to suppress crosstalk. (See Section pulse considerably longer than the minimum pulse IV-3.1.) In the other pulse systems, sufficient video length characteristic of the cut-off frequency F, or by band width must also be provided to prevent crosstalk coding it by using a train of several short pulses. In the (see Sections IV-3.2-IV-3.4). The video requirement case that a switching pulse is used for each channel(R3) puts a lower limit on carrier frequency for efficient the discrimination becomes more difficult because the operation of the power stage of the transmitter, etc. In switching pulse cannot be any longer than the off time- some cases of telemetry from small vehicles, it has been i.e., any longer than (1-1 /a)/nF seconds. It is possible possible to use effectively all or a portion of the vehicle to make use of circuits having large fly wheel effect as an antenna.(ci) This requires the use of wavelengths (low damping) to override the effect of impulse noise on of the order of magnitude of the size of the vehicle or the the synchronizing pulses provided that the impulse portion of the vehicle used and often results in a broad noise does not occur too frequently.(R3) antenna pattern as well as a reasonably broad frequency

16 M. H. NICHOLS AND L. L. RAUCH band. A broad antenna pattern is often desirable to IV-9. TRIPLE MODULATION IN RADIO TELEMETRY insure reception of signals over a wide range of orienta- Generally speaking, greater flexibility in radio telemetion of the vehicle relative to the receiving antenna. try can often be obtained by the use o triple modulaSince it is desirable to use as simple and compact tion. For example, consider a frequency division or time transmitting apparatus as is possible, modulated power 1- transmitting apparatus as is possible, modulated power division telemeter in which one or more channels carries oscillators are often used for PPM systems. For efficient a time division multiplex. Such a telemeter might operation, the video band width is limited; for example, i operation, the video band width is limited;for example, provide a number of channels capable of handling inat 300 megacycles a video band width greater than formation frequencies up to several hundred cycles per about 2 megacycles is difficult to obtain.( ) In the high second and several other channels each carrying as many second and several other channels each carrying as many UHF or microwave regions greater band width can be as thirty channels of PAM time division each sampled obtained efficiently but the antenna problem at these several times a second.(Cl) wavelengths is often troublesome because the antenna All of the considerations of multiplexing developed in must generally be on the surface of the vehicle facing the the previous sections are applicable to triple modulation. receiving station in order to obtain satisfactory re- Noise formulas can be assembled for triple modulation ception. In some cases this can be alleviated somewhat multiplying together the appropriate factors by simply multiplying together the appropriate factors by using several receiving stations at different locations e ple, consider a from Tables I and II. For example, consider a with respect to the trajectory. PAM-FM-FM system in which pulse amplitude moduMultipath transmission must also be considered. In lation frequency modulates a subcarrier which frePAM, multipath transmission can cause distortion in quency modulates a carrier.(c The Roi for this case can individual channels but in order to cause crosstalk, the be assembled with the help of Tables I and II multipath delay must exceed (1- l/a) 1/nF seconds. In PPM, multipath transmission can have essentially the 7r(r) afd\ /f\D same effect as strong impulse noise. If the signal origi- Roi(PAM-FM-FM) = i ) (IV-4) nates near the horizon, multipath effect is apt to be an \S fmi/ more pronounced and is more difficult to eliminate by ri i i i...~.' i' - ~In triple modulation systems in which a channel of a such things as direction sensitive receiving antenna, i c iii i i ii.... l ^1.'time or frequency division system is time division etc., than if the signal originates at larger elevation rate is us',. ^r l multiplexed with PAM, the sampling rate is usually angle relative to the receiver. Again the use of several rather low. Since low pass filters have not previously receiving stations distributed along the trajectory can been available for low frequencies, methods o the type been available for low frequencies, methods of the type alleviate this problem. ~alleviate this problem, described in Sections IV-1.1 and IV-1.3 are used. HowAnother consideration is that as the frequency goes Another considerat is that as the frequency goes ever, in the future, it will likely be advantageous to use up, simple antennas such as a half-wave dipole supply a t signal voltage to the receiver which is inversely pro- t ht metod that in some speal c.. Y i ^ ^' ~. ^'~ It might be mentioned that in some special cases portional to the frequency. This is because the receiving simte m.od tion-r exa s imltaneos * ^i i' i r. simultaneous modulationsfor example, simultaneous antenna grows smaller and intercepts less of the energy amltue modulation a free moulatin t..' -................ amplitude modulation and frequency modulation of the flux available at the receiving location. A receiving m f *v *is * aLLsame carrier~have been used but no such systems for antenna with large intercepting area at high frequencyhave been d l.i. l l ~ ~radio telemetry have been described in the regular is usually very directional and this is not always de- journals. sirable for telemetering work because of pointing problems. See for example reference (T1), Chapter 14. IV-10. MISCELLANEOUS REMARKS ON TIME In frequency regions where it is feasible, as far as DIVISION MULTIPLEXING technical considerations are concerned, to use any of the Television has been used for telemetering data from systems in Table II, such as around 200 megacycles if aircraft(F2) and may be classed as time division. The nF is not much greater than 104 per second, Table III procedure has been to televise instrument indications, indicates that as far as R0o is concerned, PAM-FM, flashing of lights, etc. Because of the waste space bePPM-AM, and PCM-AM are good choices. A somewhat tween instruments, on the dials of the instruments, etc., larger threshold is required for PAM-FM and for it is clear that a very large amount of useless information PCM-AM than for PPM-AM. When considering differ- is transmitted along with the useful information when ent frequency ranges, it should be borne in mind that an instrument panel is televised. In this sense, television the receiver noise figure increases with increasing fre- is a very inefficient telemeter and results in poorer quency over the range of about 50 megacycles to 1000 performance, larger power, space and weight requiremegacycles above which the noise figure is about con- ments, etc. It is certainly true that television is useful if stant. The best obtainable noise figure (power ratio) at it is necessary to transmit pictures of such things as 50 megacycles is about 2 and at 1000 megacycles about cockpit instruments, pilot reactions, etc., to an observing 10.(T1) Thus, everything else being equal, the individual station during flight or in cases in which recovery of channel signal-to-noise ratio would decrease by about a photographic records is not feasible. factor of 1/(5)a corresponding to this noise figure Instead of generating the time scale for time division change. multiplex telemetry in the airborne equipment, it is

RADIO TELEMETRY 17 possible to use pulses received from an external trans- numerical comparison will be made. Since in many cases, mitter, such as a radar, to switch the airborne com- the crosstalk requirements will limit the number of mutator.(~)0 In this way the apparatus serves as a radar frequency division multiplex channels to about ten, a beacon and telemeter with the telemeter information comparison will be made between an FM-FM tencarried by pulses interspaced with the beacon range channel frequency division multiplex and a ten-channel pulses. This could result in a reduction of airborne PPM-AM time division multiplex on the basis of equal equipment but has the disadvantage of being dependent RF band width. (This should not imply that in practice on the receipt of the radar pulse.ttt the number of channels in time division is limited to ten. All the time division multiplex radio telemeter sys- As the number of channels is increased, the advantages tems described in the literature make use of mechanical of time division over frequency division, as far as commutators or electronic commutators using standard crosstalk is concerned, become greater.) In the FM-FM tubes arranged so as to perform a gating func- system the calculations will be based on a channel with tion.(Cl M2M3,R3) However, several types of commutator deviation ratio 5 and a center frequency of 104 (see the tubes which perform the gating function for all channels second paragraph of Section 111-5). The value of A, in one envelope have been described.(G5,S3,s4) As de- from Fig. 2 is taken as 1.5. In the PPM-AM system the scribed, these tubes are generally not suitable for maximum channel information frequency, fm, is taken airborne radio telemetry because of insufficient rugged- as 100 cps and the sampling rate F is taken as ness and the complexity of auxiliary equipment such as 2.5fm= 250 per second. The radiofrequency band width channel preamplifiers, etc. It is conceivable, however, for the FM-FM is taken as 2.6fD(Kl) where fD is the full that if suitable commutator tubes were developed, a modulation frequency deviation; hence Fc=1.3fD, considerable saving in space, weight, power, and com- where Fc is the video band width of the PPM-AM plexity could be realized in radio telemetry together system. Then with increased reliability. Rop(FM-FM) =0.4. (V-l) V. Comparison of Frequency Division and Time Roi(PPM-AM) Division Multiplexing in Radio Telemetry$: The corresponding ratio of improvement thresholds is The comparison of the two types of multiplexing 10-2(W2/2)1 where W2 is the RF band width. In practice, should be based on noise characteristics, crosstalk, it may be difficult to achieve with sufficient linearity as complexity, reliability, etc. The type of instrumenta- large an RF band width on FM-FM as is feasible tion, see Section VI, should also be considered. For on PPM-AM. example, variable inductance instrumentation can be used very effectively with a FM frequency division V-2. COMPARISON OF COMPLEXITY AND RELIABILITY multiplex with few parts. One measure of complexity is the number of tubes V-l. COMPARISON OF CROSSTALK AND required per channel. The literature provides a comFLUCTUATION NOISE parison of an (AM-FM) strain gauge channel(Fl) with a (PAM-FM) strain gauge channel.(R) The AM-FM It has already been stated that in radio links suitable multiplex (14 channels) requires three tubes per channel for many channel radio telemetry from aircraft and exclusive of the radio transmitter and the PAM-FM rockets it is generally easier to provide sufficient band multiplex (20 channels) requires four tubes per channel width to keep time division crosstalk down than it is to exclusive of radio transmitter. provide sufficient linearity to keep frequency division Except for overloading the radio link and such things crosstalk down. If FM sub-carriers with large deviation as common power supplies, the individual channels of a ratios are used, the crosstalk can usually be reduced so frequency division multiplex are essentially independent that more sub-carriers of this type can be handled with -i.e., the functioning of any one channel is independent a prescribed crosstalk suppression than can be handled of the functioning of any other channel. In a time diviwith lower deviation ratio frequency modulated sub- sion multiplex, all channels depend upon the functioning carriers or with amplitude modulated sub-carriers. In (and synchronizing) of the commutators. In some order to get a number of wide deviation ratio sub- cases(M3,R3) the commutator is made up of a chain of carriers into a reasonable frequency band, the maximum trigger circuits, one for each channel. In case any of information frequencies in the individual channels must these circuits fails, all the following channels in the be limited. sequence may be affected. Thus in these types of time The fluctuation noise comparison can be made with division there appears to be more chance for failure than the aid of Tables I and II. As an example, the following in frequency division. In cases of sufficiently slow time division it is sometimes feasible to record essentially the ttt It might also be mentioned that frequency division can be video output so that if synchronism of commutators is used in a doppler radar channel in which case the radio carrier is l a r u filtered out togive the doppler shift. lost, a record is still obtained although laborious to $t For a qualitative comparison, see reference (H3). reduce.

18 M. H. NICHOLS AND L. L. RAUCH TABLE IV. Tabulation of telemeter systems described in detail in the literature. Number of samples per Frequency Number of Carrier Number of second per response per tubes per frequency Reference Type channels channel channel channela in megacycles Remarks (R3) PAM-FM 18 952 200 cps 4 Not specified Includes amplifiers with sufficient gain for strain gauge instrumentation. (C6) PAM-FM 16 6400 2240 cps 1.7 200 The system may be altered to provide 32 or 64 channels at sampling rates of 3200 and 1600, respectively. (F1) AM-FM 14 200 cps 3 70 Includes amplifiers with sufficient gain for strain gauge instrumentation. (H2) PPM-AM 23 190 2+ 1000 Voltage input range 0 to 5 volts. Channels sampled at irregular intervals depending on information in previous channels. (M3) PPM-AM 30 312 2+ 1025 Voltage input range 0 to 5 volts. (M2) FM-FM 6 60 cps 1 or 3b Not specified * Exclusive of radio transmitter. b Depending upon type of instrumentation. At this point it seems appropriate to list in Table IV sider the problem of instrumentation for telemetry of the telemeter systems which have been described in secondary importance. In fact, it is the authors' opinion detail in the literature. It is to be noted that the largest that too little attention has been given to instrumentanumber of frequency division channels listed is 14;(F1) in tion and, as a result, the instrumentation development this case the paper(Fi) does not include a quantitative has in some cases lagged the other more electronic dediscussion of the crosstalk in the system nor does the velopments. For convenience in discussion, the instrupaper state the modulation level at which it was mentation is divided into several groups as follows.~~ possible to operate the FM transmitter.ANCE WIRE STRAIN GAUGE TYPE VI-. RESISTANCE WIRE STRAIN GAUGE TYPE OF INSTRUMENTATION VI. Instrumentation for Radio Telemetry The resistance wire strain gauge is an instrument It is necessary to convert the quantity to be measured ose resistance changes upon elongation of the resistwhose resistance changes upon elongation of the resistinto an electrical signal which eventually modulates the a w ance wires which make up the gauge.(Rl4) It is inherent, radio link. In this paper, the apparatus which performs then, that the fractional change in resistance is smallthis conversion is called an instrument. then, that the fractional change in resistance is smallthis conversion is called an instrument. about two percent maximum. This is a decided disSince the principal use of radio telemetry is for flights i e. r J * i e ^ ~ J1 T ~ eadvantage but its other advantages in the measurement testing of aircraft and rockets and for upper atmosphere i n r research, the remarks in this section are confined to o s r r 1 * * * * 1 outweigh this disadvantage. Unbonded strain gauges are these fields. Because of the limitations in space, weight, outweigh this disadvantage. Unbonded strain gauges are and power and the extremes of temperature, vibration, also used in pressure gauges, accelerometers, rate of turn etc., which are often imposed on the entire airborne indicators, etc.'(FR 6M5) The resistance wire strain apparatus, it is desirable to choose a method of instru- gauge is usually used in an AC bridge circuit. The output mentation which will meet the requirements with a of the bridge is thus amplitude modulated by the minimum of complications such as high gain amplifica- information. If the bridge is fed by a sub-carrier osciltion, sensitivity to vibration, etc. It is not the purpose lator of fixed frequency in a frequency division system, of this paper to enumerate or discuss the various the result is an amplitude modulated sub-carrier. In a methods and types of instrumentation in use in radio time division system it is convenient to excite the strain telemetry. However, in the interest of completeness, the gauge bridge by an alternating voltage whose frequency following remarks on the types of instrumentation used with the different types of multiplexing are included. ~~ For a general discussion of instrumentation, some of which is The reader should not infer from the small space given applicable to radio telemetry, see Roberts (reference R14). For a qualitative discussion of instruments in telemetry and aircraft to instrumentation in this paper that the authors con- control see Kiebert (reference K4), and Andresen (reference Al).

RADIO TELEMETRY 19 is locked in with the transmitter commutator so that the cision and output torque, servo type null instruments amplified output of the bridge is sampled at the crest.(R3) have been developed.(DIE2) Another application similar to the strain gauge is the resistance thermometer(F) which can be handled in the VII. Recording in Radio Telemetry same way. It is usually necessary to obtain records of the reVI-2. VARIABLE INDUCTANCE TYPE ceived information in permanent or semipermanent Vl-2. VARIABLE INDUCTANCE TYPE INSTRUMENTATION form during the flight. There are many ways of recording such as by photographing cathode-ray tube displays, In the cases of pressure and acceleration measure- photographing electric meters, pen and photographic ments, the variable inductance type of instruments have recording galvanometers, magnetic tape and wire rean advantage over the strain gauge type in that a much corders, etc. The pen recorders (or equivalent) have an larger fractional change in inductance can be ob- advantage of requiring no photographic development tained.(Cl M2 P2) For example, t20 percent change is but they are limited in frequency response and require feasible.(P2) The variable inductance instrument can be relatively high driving power and sometimes under field used in a bridge circuit or it can be used directly as the conditions the pens cause trouble by clogging. The inductance in an LC frequency modulated sub-carrier magnetic tape recorders are used mostly for recording oscillator.(clM2,P2) In general, the variable inductance FM sub-carriers or the entire FM sub-carrier multiplex; strain gauge is much less convenient to use than is the the records are subsequently played back, demodulated, variable resistance type described in the previous and recorded in one of the above forms. In this type of section.(P2,H1) The variable inductance principle has also recording, special care has to be taken to correct for been applied to shaft position indication in connection "wow," and if a sub-carrier multiplex is recorded, with controls, pointer indications, etc.(cM2,P2,SlR7,R8) special attention has to be given to linearity. When a VI-3. POTENTIOMETER TYPE INSTRUMENTATION large number of channels are telemetered it is usually desirable to record as many as possible on the same film Shaft position measurement can often times be carried or paper so as to have a common time scale; if more than out by connecting a simple potentiometer onto the one film or paper is required, it is generally necessary to shaft.(C'M2,R3 Special low torque potentiometers have record a time scale on both records in some convenient been used in connection with regular aircraft cockpit form so that the records may be aligned in time with instruments, indicating pressure gauges, etc.(ciR9g,R) minimum effort. The potentiometer can be connected across a sub-carrier The process of reducing records is frequently long and oscillator thus providing an amplitude modulated sub- expensive in both manpower and delay. The usual procarrier,(FL) connected as a rheostat in the phase shift cedure is to measure the displacement of the individual network of a phase shift oscillator providing a frequency channel record from a base line, apply an instrument modulated sub-carrier,(Cl M2) or connected across a volt- calibration curve, and then plot as a function of time or age source to provide a variable voltage for modulating set down the data in tabular form. There are many aids a time division multiplex(R) or for frequency modulating to this process of various degrees of automatic form a sub-carrier oscillator as in the next section. which are immediately apparent. For example, in order VI-4. VOLTAGE TYPE INSTRUMENTS of increasing departure, these might be: (1) visual aids for record reduction; (2) a stylus manipulated by an The voltage output of a potentiometer, as described operator so as to follow the record of a single channel in the previous section, or other source of voltage has having mechanical (or electrical) linkages which autobeen used to frequency modulate a sub-carrier.(C'M2) matically inject a correction from a calibration cam and Many other instruments such as Geiger counters, then record in tabular, punched card, or plotted form; ionization chambers, ionization pressure gauges, Pirani (3) automatic electromechanical or electrical injection gauges, etc., provide a voltage output which can be used of calibration curves during the flight with recording by to modulate a sub-carrier or a time division multiplex. conventional means and/or during flight coding and The principle of magnetic amplification(Cl) has also been recording in digital form. The recording in digital form found useful in telemetering currents such as from may be played back in order to punch cards, print the thermocouples. data in tabular form, or fed into a digital computer. In the case of recording in digital form, the remarks on 5. MISCELLANEOUS REARKS ON INSTRUMET quantization noise in Section IV-5 are applicable. The design and application of accelerometers has been In the authors' opinion, at least at this stage of dediscussed by Weiss.(W2) A vacuum tube acceleration pick velopment of telemetry, a continuous recording of all up has been developed by Ramberg.(Ri2.n2) For a brief channels as a function of time is desirable regardless of history and discussion of application of magnetic ampli- other types of recording, such as in digital form, autofiers see Greene,(G4) Logan,(L4) etc. A transistor oscillator matic injection of calibration curves, etc., which may be circuit for frequency modulated sub-carriers has been carried out simultaneously. The reason for this is that described by Lehan.(L3) In order to obtain higher pre- there is a need for editing of the record to check on such

20 M. H. NICHOLS AND L. L. R1AUCH things as fading of the signal, crosstalk, and other distortion will be negligible. Let us assume it has been imperfections which are easily discernable when the determined that the distortion of the input signal f(t) channel records as a continuous function of time are is negligible when If(t) I $ D where D is a positive conexamined simultaneously. stant. Let us also assume the worst possible condition in which the output signal g(t) is given by g=f for VII-1. AIRBORNE RECORDING I| fi D, g=D for f> D, and G=-D for f<-D. That Airborne recording by such means as recording gal- is, the characteristic is perfectly linear with unit gain vanometers, photography of instruments, etc., has been between -D and +D and the radio link completely extensively used in flight test work.(B7, c EI L6, P,s7,w) limits signals outside of this range. Some equipments It is the authors' opinion that, wherever airborne have characteristics approximating this, particularly recording is satisfactory under flight conditions and re- when inverse feedback is used and the final amplifier covery of records after flight is feasible, airborne stage overloads. recording should be used in place of radio telemetry. The distortion that results when Ifl > D may be However, there are many cases in which the recovery of thought of as an error signal of value g-f introduced records is a problem or in which operating conditions into the output of the radio link. Let the input signal and space and weight requirements can be more effect- f(t) be the linear sum of a number of sinusoidal subively met by radio telemetry. In certain cases in which carrier signals, the sum of whose amplitudes is just a space and weight are available, it has been found little greater than D. Then it is clear that during most of desirable to use both airborne recording and radio the time If(t)\ (D provided there are only random telemetry in order to increase the probability of ob- phse relations between the sinusoidal components. taining a record and in order to permit checking the two Only occasionally will the relative phases of the comsources of data against each other, ponents be such that [f(t) i becomes nearly as large as Recent developments in compact magnetic tape or the sum of the amplitudes and so exceeds D. wire recording have reduced the size and increased the Thus the error signal will be zero most of the time ruggedness of airborne recording equipment.(B6.K2) If a with occasional negative or positive pulses of short quantitative record as a function of time is desired, it is duration. The frequency spectrum of these pulses will best to modulate a carrier; frequency modulation seems generally be wide enough to cover the sub-carrier pass to be the most satisfactory. If a record of the time oc- bands uniformly. currence of pulses, the height of which is unimportant, is VIII-1. CRITERION FOR TOLERABLE CROSSTALK desired, it is possible to modulate the tape or wire directly. A criterion proposed by Hollbrook and Dixon(Hm) for maintaining crosstalk at acceptably low levels is that VIII. Crosstalk from Overload in Frequency- the error signal shall be non-zero during an average of Division Multiplex Radio Links not more than 10-3 of the time. This has been verified experimentally for certain conditions. T As an approximation we shall assume the nonlinear This criterion leads to definite relations giving the distortion to be of a simple type where the distortion is a permissible amplitude of the sub-carriers as a function function only of the instantaneous signal at the input of of the number n of sub-carriers and the overload value the radio link. I II For sufficiently small signals the D. To obtain such a relation it is first necessary to know the probability density function p, for a signal con111 The concept of overload in an amplifier or radio link is not sisting of the sum x of n sinusoidal components with a simple one. What is usually meant by overloading is that the random phase relations. For a single sinusoidal comdevice ceases to act as a linear four-terminal network. By a linear ni four-terminal network we mean a device which operates linearly ponent of unit RMS value this is(L upon an input function of time f(t) to give an output function of time g(t). That is, the superposition theorem holds. Mathe- 1 /pl(x) =_______ (x2/)~ x2<2, matically this is expressed by g(t)=J: f(r)h(t-r)dr where h(r) P1~= [ (x- /2)X' (VII-1) determines the linear operation and h(r)=0 for r<0. Accordingly, the deviation from linear response is usually not expressible as a p(x) =, x2> 2. simple plot of instantaneous output as a function of instantaneous input which deviates from linearity for sufficiently great inputs, circuit as a simple nonlinear function of voltage or current indeFor example, in the case of sinusoidal inputs the amount of non- pendent of time (FM and PM radio links are exceptions). Howlinear distortion is not only a function of the instantaneous input, ever, after linear networks are placed on both sides of the simple but also often a function of the frequency. In the case of a pulse nonlinear element we have the general situation described above. the nonlinear distortion may depend on the rise time and duration This frequency-dependent nonlinear distortion in radio links de(frequency spectrum) as well as on the height. It is well known in pends very much on the circuit adjustment and design of a parthe case of frequency modulation radio links that with sinusoidal ticular unit and there are no general rules describing it for parmodulation of a given amplitude the nonlinear distortion increases ticular methods of modulation, etc. as the modulating frequency is increased.(R3) This effect is empha- ~~ See reference (H5) page 634: "Experiments have been sized even more in phase-modulation radio links and is present to conducted on a number of different multi-channel amplifiers, each a certain extent in amplitude-modulation radio links. It is true loaded by various numbers of active channels all at the same that the nonlinear response often originates somewhere in the volume."

RADIO TELEMETRY 21 - "'_/n(C1dD)s.I - _ It has been shown that the normal form is a fairly.' LD] good approximation for p,(x) when n> 10 and it grows [4 _ __ [ _ [_ 7_ _ _ _~_ _~'_'better as n increases.(L5) Figure 3 is a plot of D as a /D - I+.-l function of n for -C(D)= 0, 10-4, 10-, and 10-2. For ~ ~ ~~ -~ -. _ _ _ _ _ _ _ _ _ l l _ n 10 the curves have been calculated by using the I ^ ""'" i_ ___ c,, -i-'"1 proper non-normal forms for p,(x).*** The curves for ~ _ ~_ _- _ —~ ~_-_ —-~ ~ - -.104 and 10-2 are included to show that the overload ____/^~~~~~ j ~~ value D is not very sensitive to the magnitude used for ~_~_~_ __ ~ _, - _ _ the crosstalk criterion. The solution of 1-C,(D)=0 FIG. 3. Overload value D exceeded by n sinusoidal subcarriers corresponding to no overload is of course D= (2n)1. of total RMS value unity [each sub-carrier of amplitude (2/n)-] In order to better visualize the improvement offered during a fraction of the time 1-C,(D) equal to 0, 10-4, 10-3, by the crosstalk criterion over the simple requirement of and 10-2. no overload Fig. 4 is a plot of the sub-carrier amplitude. L.'1^ ~.r~ ^ ~improvement ratio An obtained by use of the overload That is, the probability of the instantaneous value o d b u o t falling between x and x+dx is p (x)dx. criterion. A, is the ratio of the sub-carrier amplitude falling between x and x+dx is plx)dx. fallin bewe x an xd i p(xd. \ Ipermitted by the overload criterion to the sub-carrier For n> I the formulas for pnox) rapidly become very For n> 1 the formulas for (x) rapidly becoe v ampleitude permitted by no overload. Figure 4 is obcomplicated and for n>2 pn(x) is not expressible in. Figure 4 is obcomplicated and for T 2 T. istained from Fig. 3 by dividing the ordinants of the curve terms of the elementary functions. However it can be t from F, g. by the ordi nants of the curve shown that(LS) for Cn(D)=l by the ordinants of the curve for shown that (L6 Cn,(D) = 1-10-3. 1 r0 /n\ p(x) =- cos(-) xtJon(t)dt, (VIII-2) VIII-2. JUSTIFICATION OF THE CRITERION,r~ d ~o \ 2,~ ~As far as the authors know there has been no theowhere Jo(t) is the zero-order Bessel function and the retical justification of the above criterion for crosstalk amplitudes of the sinusoidal components are equal to due to overload (Cn= 1-10-3). We shall attempt to (2/n)l so that the resultant sum has unit RMS value. obtain an approximate formula giving the ratio of the The probability that I xl D is RMS crosstalk disturbance to the desired signal in any channel of a sub-carrier multiplex system when the Cn(D) pn(x)dx. (VIII3) number of channels is large. That is, we assume -D 1 x2 Substituting from (VIII-2) gives, after integration with Pn(x) =( exp 2) respect to x, 2/2 a sn(n/2)2Dt 0The mean value M of the error signal is Cn(D) =-(- jwJonjt)dt. (VIII-4) 2 o Xx2 n t M=(~) exp( —)(x-D)dx Formulas are available for the case of unequal ampli- tudes of the sub-carrier components,(L6) but we shall =2.79X10-4 (VIII-7) limit this discussion to the case of equal amplitudes. for D= 3.29. In accordance with a well-known theorem of mathematical statistics(H4) the probability density function' l 1 approaches the normal form as the number of sinusoidal components becomes large. That is lim p,(x) = exp - - =p(x) (VIII-5) / -oo (27r) \ 2/ where the signal has unit RMS value. The crosstalk i criterion determining D becomes' o0,,oo /2\ i D ( X2\ FIG. 4. The sub-carrier amplitude improvement ratio A, as a 2 J I 1) r 4 - largest sub-carrier amplitude which will cause overmodulation Pn 0 of the time to the largest sub-carrier amplitude which will cause no overmodulation at all, assuming all sub-carriers to have the same Reference to a table for the error integral provides the amplitude. result D= 3.29. Thus the overload value is 3.29 times the RMS value of the signal provided the number of com- *** The authors are indebted to Professor W. C. Johnson of Princeton University for the calculations for small n involving the ponents is sufficiently great. non-normal forms.

22 M. H. NICHOLS AND L. L. RAUCH Now the expected number of maxima per second of RMS crosstalk disturbance to the RMS sub-carrier the absolute value of the total signal exceeding the value signal is 0.00475 or about one-half of one percent of full D is approximately modulation. Thus the crosstalk criterion appears to D22 have a reasonable theoretical basis. (5)exp — _-fv =3.47X 103fv, (VIII-8) Additional reasoning based upon the non-normal \ 2/ distributions for small numbers of channels shows that the criterion results in a smaller crosstalk disturbance where jv is the upper frequency limit of the low pass when the number is small. Thus the criterion band.occpie by th su-are chnes iR1i Thi i when the number of channels is small. Thus the criterion band occupied by the sub-carrier channels.(Ri3) This is ^^-. J1.i~ ri i' can probably be relaxed somewhat when the number of very nearly the expected number of pulses per second in can al la sm a m the error signal and is based upon the approximation i,^~,T_~ ~ ^ f, ~.^.., It should be pointed out that the above result was that the energy of the sub-carrier channels lying in thee ce su frequency. u..1'p to. isdistributeduniformly obtained on the assumption of complete saturation of frequency range up to fv is distributed uniformly thogu th f requency range u o. Dis disbted unior. M. the signal for absolute values greater than D. In practice throughout the frequency range. Dividing this into M throughou the f lrequenc rangte Diidngrao thei intoe M this saturation is not complete so that the above result provides the result that the mean area of the pulses composing the er g., should be considered an upper limit for the crosstalk composing the error signal is 0.0804/fv. disturbance. Since we do not know the distribution function for the area of the pulses let us make the approximation that IX. Crosstalk Due to Restricted Bandwidth in the pulses are of equal areas and equal to the above Pulse-Amplitude Modulation Multiplex mean area. As previously pointed out most of the pulses Systems are short compared to the envelope rise time of the channel band-pass filter. This means that the envelope Crosstalk as a function of band width in PAM of the pulses at the output of a filter will have the shape multiplex systems has been studied by Bennett.(B2) characteristic of the impulse response of the filter, Results are obtained by studying the Fourier series whatever the shape of the short pulse at the input. Also representation of the periodic PAM multiplex signal. In the area of the output pulse envelope will be the same as this section we extend the calculations in Bennett's the area of the input pulse. paper using a different method. An approach which In the case of an "ideal band-pass filter" with the ith appears to lend itself better to calculation is by means of sub-carrier located at the center, the shape of the output the nonperiodic transient response due to the transfer envelope of the pulse is given by(G2) characteristic of the restricted band width. Except in cases where the number of channels is so small or the ( sn2r= fit band width so restricted that the transient response is 27rff t'prolonged beyond an entire frame period of 1/F, the transient approach must give the same answer as the where ffi is half the band width of the ith filter and periodic approach.** provided the pulse is small relative to the sub-carrier. We assume an ideal low pass filter with cut-off freThis has a mean value a/2f/i and an RMS value quency knF and no phase delay.~~~ This is equivalent in a/(2ffi)1. Thus the RMS value is (2ff/i) times the mean the periodic approach to neglecting all frequency comvalue. Multiplying this by the mean area of the pulses ponents above knF. It is easy to calculate that a pulse of we obtain for the RMS value of each pulse disturbance unit height beginning at t=0 and ending at t= l/anF in the ith channel comes out of the filter with a functional form f(t) where ~(f i) 1 1 0* ~ 11y f(t) =-Si(27rknFt)-Si 2rknF (t- (IX-1) r^ (K anFJ Since the individual disturbances occur on the average at the rate of 0.00347fv per second, the RMS value of w the total crosstalk disturbance in the ith channel is t sinx Si(t) = dx. 0.00672( -) (VIII-9) fJv We assume the measurement of the pulses is by means In the case of AM sub-carriers of equal band width we of area as when low-pass filters or pulse integration is have approximately used.t:t- The area of the wanted signal in any channel at /fi\ 1 I** Actually the transient approach gives the same answer as l = (VIII-10) the periodic approach under all conditions provided we include V fv. (2n)f the transient disturbances from all of the preceding samples of the crosstalking channel instead of from the first preceding sample assuming no guard space between channels. The RMS alone. a~~~ For other transfer characteristics see reference (M6). value of each sub-carrier is 1/(n)i so the ratio of the it: See Appendix 4.

RADIO TELEMETRY 23 its maximum value is crosstalk indicated by a vertical dashed line. The frellct/a~nF ~quent changes of phase are due to the ringing of the ~ I f(t)dt assumed ideal low pass filter. Due to the simple form of t- 6 fo odpi for a= oo in (IX-6) it is not presented as a figure. However for reference the function 1/27rk is plotted in and the area of the crosstalk signal in the mth following terms of attenuation in Fig. 5a (in addition to P1 for channel corresponding to maximum signal is (m= 1 for a= 1). This is the locus of the attenuation minima of pi adjacent channel) for a= oo. The points of infinite attenuation occur at half-integer values of k. Calculations of pi for a=20 1Cm/' nF ^ ( \ / show it to be the same as for a = oo within 2 db for k < 6. 1 r=Jn f(t)dt. (IX-2) Calculations show pi for a= 10 also to be closely the same as for a= oo until k)4. When k=6 the a=10 Thus the ratio of the maximum crosstalk in the mth value of pi has become approximately 9 db greater than following channel to the maximum signal in that the a= oo value of pi. channel is The general characteristics of the crosstalk attenuaYm tion plots are as follows. As a increases above unity, the Pm =. (IX-3) attenuation plot rises very rapidly along its entire length Y7 until at a= 1.11 the average rise is approximately 10 db. Substitutingfor in(I-2)andchangingvariables The rise for 5<k<6 is considerably greater than the Substituting for f(t) in (IX-2) and changing variables and limits gives average. As a increases to 1.43 the plot falls at small values of k and does not change significantly for larger 1 rt(ma+li)/anF (ma-1)/anF values of k. As a is increased to 2.0 the plot falls slightly Tm=-L + for small values of k and rises for 5 < k< 6. As a increases ITL "0 to 2.86 there is no significant change for k<6. Eventum/nF ally as a is increased the plot falls below the a= 1 level -2 S](2TknFt)dt. toward the a= oo curve of Fig. 5a. However, no matter If we define how large a finite value of a is chosen the plot will r^t t always rise considerably above the a= oo level for Sii(t) = Si(x)dx sufficiently large k. o then X. Information Efficiency of Pulse-Time i1 1 1 ] Modulation and Multiplex', 2k Sni27.rk(m+- Methods 2rknF L V a/.1 The information capacity of a transmission channel Irm/ l\1 I 2i2 ) X depends upon the band width and signal-to-noise ratio +Sii 27rk m —) 2Sii(27rkm) (IX-4) available. The information capacity I in bits per second a J c xis given by For convenience in calculation we use I= W log2(1+R2) (X-1) where W is the band width and R is the RMS signal-toand 7Ym* = 27r2knFym noise ratio.(s6) A bit is the basic two-valued unit of TY m* information often represented by a binary digit as in Pm. (IX-5) PCM. Equation (X-l) holds only for noise with a white To* frequency spectrum and a Gaussian probability distribution. F~or ca= xo this reduces to From (X-1) it is clear that transmission channels with sin27rkm different band widths and signal-to-noise ratios can have Pm = -__. (IX-6) the same information capacity. For I constant and R 2xrkm large compared to unity we have the result that when the band width W is increased by the factor k the signalA table of Sii(x) has been computed*** and used to to-noise ratio R becomes Rl/k. Many of the modulation calculate the data in Figs. 5a through 5e for the adjacent methods in current use take advantage to some extent channel crosstalk ratio pi. For convenience the crosstalk of this possibility of exchanging band width for signalratio is expressed in decibels as crosstalk attenuation. to-noise ratio. The original information consists of a The solid points indicate in-phase crosstalk and the open signal with a certain band width and required signal-topoints out-of-phase crosstalk. It should be noted that at noise ratio. The signal-to-noise ratio of the transmission each change of phase there is a value of k giving no channel turns out to be less than that required by the *## Copies of this table are available from LLR. original information signal. So the information signal

24 M. H. NICHOLS AND L. L. RAUCH 60-... -. -- I T ~~ db I I 40 I= I db. ~ Mx 1..' I I I I I I, H W 40 ~ ~ - - _ -.-~ ~ -^ ~ J ~ ________3 4 5 6 Ik< I * I j ~, i II I I i I1 j I I Idb'~~ ~ II I IC 81)i III I I I I _6 I I ~ 60 __2 _3 4 5 6 7' 2 6 (b) ) _______ 60 I 4 kI 6 II I1.11 I I I _____ ______2_-4~- j__l..-j-I' -I-~_ __ db 1 1'1-1r I I ~ ~ -- ~ ~ ~ ~ ~ ~~I~~~~~ -I I 8Io I I.. (L4LL., I I ~ I I~ ~ "a l (e) 4 - I -. ________FIG. 5. Crosstalk attenuation in decibels as a function of I ~Ij~ ~~ ~ ~~ ~ ~ ~frequency in units of nF for various values of alpha as ~ ~~I I I ~~follows: (a) a=land oo, (b)a=1., (c)a=1.43,(d)a=2, (e) a= 2.86. Solid points represent in phase crosstalk and 0 I I circles out-of-phase crosstalk. The dashed vertical lines ~i~~ ~~ I-~~~~ iI~ ~(drawn in by inspection) separate regions of in phase cross1 i I talk from regions of out-of-phase crosstalk where the ~ i*~~~~~~~~~~~~~~~ attenuation is infinite. 60 I' I 3 4 5 6 7 k (c) is subjected to a nonlinear operation (modulation) which ratio reduction obtained. Another way of saying this is results in a new information signal containing the same that the information capacity of the transformed information, but requiring a larger band width and (modulated) signal channel must be greater than the smaller signal-to-noise ratio. At the other end of the information capacity of the original signal channel. transmission channel the original information signal can Frequency modulation is very poor in this respect while be recovered by use of the inverse nonlinear trans- pulse-code modulation is very good though not perfect. formation (demodulation). Sometimes it is not de- To compare the various modulation methods Table VI sirable to recover the original information signal and the gives the information efficiency for each method in transformed signal is used directly as in PCM data terms of the desired channel signal-to-noise ratio R1. storage. Information efficiency is the information capacity of the None of the so-called noise improvement modulation original signal channel divided by the information methods in current use take full advantage of the band capacity of the modulated signal channel. It is clear that width and signal-to-noise exchange offered by (X-l). the ideal information efficiency is 1.0. From (X-l) it The various modulation methods require a larger band follows that in considering multiplex methods, it is width than required by (X-l) for the signal-to-noise proper to add the information capacity of several

RADIO TELEMETRY 25 TABLE V*. Before modulation (after demodulation) After modulation (before demodulation) Modulation Band width Signal-to-noise Signal-to-noise Band width Signal-to-noise Signal-to-noise method Wl Ri at threshold Ri* W2 Rt at threshold R2* S I S 1 PAM-AM nfm'- 16nffm k2 (nfm)1 k2 2(2nfm) S 7fD fD S 1 PAM-FM nf,, -. 1.26 2.6f - 2.8 k2 8ntfm niflf k2 (1.3fD) S (Fc) F, S 1 PWM-AM nfmn - 2.83- 2Fc -- 4 k2 V/nfm nfm k2 (F&)i S v3fD fD(D)4 S 1 I'WM-FM nf m 4.50- 2.6fD -. 2.8 k2 nfm(Fc)i nfm k2 (1.3fD)l S 5F, F, S 1 nm PPM-AM nf.m 3.54 2F, 8( k2 8nifm nfl, k2 (F,) \ F, S 1 PCM-AM nfm, * 2N 1.22 2N 2Nnfm - 5.65 k2 (nNf )i S _ fD f S 1 FM-FMb nfm - 2.3 / 6.05 — 2.6fD -* 2.8 k2 nflf" nflfmt k2 (1.3fo) In constructing this table from Table II we have used the relations a =2, F -2fm, F, =4nF. r -4n, and FD -DF,. bIn the FM-FM case, it is assumed that the carrier threshold governs. The following relations are used for the center channel: aOi/S =2.32/(n),. fi =f,. fi =fD/2D, and fdi =fD/2nD. channels with the same signal-to-noise ratio by adding It should be noted that where an AM carrier is indithe band widths of the channels. cated it has been assumed that double sideband As an intermediate step to Table VI, Table V gives transmission is used. If single sideband transmission is the band widths W1 and W2 and signal-to-noise ratios used instead, the information efficiency will be increased R1 and R2 before and after modulation (after and before by a factor 2. demodulation) based on the data of Table II. The TABLE VI. FM-FM case from Table I is included for comparison purposes. 1 log(l+R12) The information efficiency E is given by PAM-AM - 16 Rog + R) E W log(l+R2) log E = (x-2) 8 W2 log(l+R22) 0.48 PAM-FM -- log(l+R12) where the common base of the two logarithms may be as Ril desired. In calculations we shall use the base 10. Now R> R2 in all cases where noise improvement is obtained PWM-AM - log(l +R12) including PAM-AM. Therefore, the maximum value of R1 E is obtained in all cases when the common factor S/k2 1.83(D)I is made as small as possible. In all cases except PAM-AM PWM-FM log(1 +R12) this is when S/k2 has the improvement threshold value R as given in Table II. 1.77 log(l+R12) The values of R1 and R2 obtained by using the im- PPM-AM provement threshold values of S/k2 are denoted re- logfl +spectively by R1* and R2*. These are also listed in \ Ri Table V. log(1 +Rl2) In Table VI the information efficiencies are given in PCM-AM 0.10. terms of the signal-to-noise ratio R1 of the original logRI-0.088 information transmission channel. Except in the case of 2.86 PAM-AM, it is assumed that each system is operating FM-FM -log(i+R1i) at its improvement threshold.,

26 M. H. NICHOLS AND L. L. RAUCH APPENDIX 1 used instead of the rise time of a step, the expression for the wide band improvement Roi becomeslb WIDE BAND IMPROVEMENT FOR PWM-AM AND PWM-FM R SF, Roi~- F- (2-1) 4ntF' In PWM-AM the radio transmitter is turned full on for a length of time proportional to the instantaneous value of the signal. It is The response of an ideal low pass filter of band width Fc to an assumed that the duration of the pulse is measured from a precise impulse at t=0 is, neglecting time delay, time reference (i.e. no noise on the time reference) to the point sin2irFt when the voltage has decayed to one-half its full on value (i.e. a 2rF (2-2) half-height slicing). It is also assumed that the sampling takes place at regular intervals. In deriving the wide band gain for this where a is the maximum height of the impulse response. To obtain method, the theorem proved in Appendix 5 is used. The RMS the improvement threshold we calculate the RMS value of a PPM noise in the video is k2(F),i. From reference (G2) page 75, the slope signal consisting of these impulses occurring at the rate of nF per of a step function at the half-height is 2hF, where h is the height second. The RMS value of a single impulse is of the step function. Therefore the RMS time fluctuation at the / sin22rFidt a half-height point due to the video noise is k2(F),,/2hF,. If the duty a 4r - dtJ =-~. (2-3) factor of the transmitter is assumed to be j then h=V2v2S. If the 2 (2 peak to peak variation of the pulse width due to the information For nF impulses per second this becomes modulation is 1/nF, the corresponding RMS value is 1/V22nF. S=a(nF/2F,) (2-4) Therefore, the video signal-to-noise ratio may be written S(2F)i where S is the RMS video signal. (1-1) At the improvement threshold the impulse height a should be 2 nk2F times the peak noise which we assume to be 4 times the RMS In applying the theorem of Appendix 5, the pulse widths may be noise. Thus considered as an instantaneous time series, in which case the a=S(2F,/nF)= 8k2(F,)i. (2-5) signal-to-noise ratio after passage through a low pass filter with So at the improvement threshold the RMS signal-to-noise per unit cutoff at fm is band width ratio in the video channel is nk2F f J (12) = 42(nF). (2-6) k2 Division by the signal-to-noise ratio, S/k2(fm)' of the comparison" Since double sideband AM transmission is assumed, we have for single channel AM link gives the wide band improvement Roi for the RF channel an RMS signal-to-noise per unit band-width ratio PWM-AM. of Ro= I/n(F./F). (1-3) (2 4(nF)i. (2-7) If it is considered that the improvement threshold occurs when the crest fluctuation noise in the video equals half the pulse height APPENDIX 3 i.e., when VM4k S IMPROVEMENT THRESHOLD FOR PCM-AM 2 The RMS signal-to-quantization noise ratio in the channels the improvement threshold is is(B3) S/k2=4(F,)i. (1-4) /. 2N. (3-1) In PWM-FM, the FM carrier is switched from full modulation to To obtain the improvement thresholds, we note that on the one side of center frequency to full modulation the other side for average approximately half of the possible NnF pulses per second a length of time proportional to the instantaneous value of the do not occur. We assume the pulses to be of width 1/NnF with a signal. Proceeding as in the case of PWM-AM, taking into account rise time of 1/NnF since crosstalk is not important. Thus the the triangular FM noise spectrum, the Roi turns out to be height of the pulses is v2S and the video band width is NnF/2. (12) (6)iD F, Equating the pulse height to 2 times the peak noise gives Rot= F (1-5) i (1-5)~ ^v'2S=8ksM= )2 (3-2) where D is the carrier deviation ratio. If it is assumed that the carrier FM improvement threshold governs, then the improvement S4(Nn _= 4(NnO (3-3) threshold is (see Section III-2) k4 S/k2= 3.2(fD)i. (1-6) for the improvement threshold in the video channel. For the RF In the above derivations it has been assumed that the instan- channel this is taneous sampling takes place at regularly spaced intervals whereas 2V2(NnF)*. (3-4) in practice a triangular timing voltage is usually used which displaces the sampling time in accordance with the voltage of the APPENDIX 4 signal. (K) In the case of many channels the correction for this is small. INTEGRATION OF PAM SAMPLE PULSES It is clear that if the integrated value of each sample pulse is APPENDIX 2 used rather than an instantaneous sample taken at some time during the pulse, the fluctuation noise will be reduced. In the WIDE BAND IMPROVEMENT ANDue IMPROVEMEN following we determine exactly the extent of this noise reduction due to pulse integration. Goldman^ has obtained an expression for the wide band im-,Goldman has obtained an expression for the wide band i.- 2b L. L. Rauch. "Fluctuation Noise in Pulse-Position Multiplex Systems," provement of PPM-AM. If the shorter rise time of an impulse is 1946; privately distributed paper prepared for Melpar. Incorporated, and the Applied Science Corporation of Princeton. l* See reference (62) page 249. ~~ L. L. Rauch, "Noise in Pulse-Code Multiplex Systems," 1946; privately'a See reference (G2) pages 280-283. distributed paper prepared for the Applied Science corporation of Princeton.

RADIO TELEMETRY 27 The result is that the noise reduction due to pulse integration is Finally exactly that obtained by passing the sample pulses of a given 1 -exp[- (iw/nF)] channel through a low pass filter of cut-off frequency F/2. This nFs(). (4-7) result clarifies the twofold action of the low pass filter. It first produces a noise reduction due to its integrating action on the It is now evident that C(t) is obtained from g(t) by the transfer produces a noise reduction due to its integrating action on the function pulses. Its second action is then the smoothing of the integrated function pulses. In agreement with the above, if a low pass filter is preceded T() = nFexp(i/nF) (4-8) by pulse integration there is no improvement over the low pass iw filter used alone. Straightforward calculation gives Before proceeding with the derivation it is necessary to define in(w/2anF) what we mean by "RMS value of the pulse signal." This is the T(w) = 2F exp[-(i/2anF). (4-9) standard deviation (in the statistical sense) of the time series whose terms are the values associated with each sample pulse. These Thus the amplitude factor is values may be the integrals of samples of finite duration or they sin(w/2anF) may be the heights of instantaneous samples. The integrals of (w/2anF) samples of finite duration are always normalized by dividing by the length of the sample. It immediately follows from the above and there is a simple time delay of definition that the RMS value of the instantaneous samples of a/2nF continuous noise signal is exactly equal to the RMS value of the continuous noise signal. which is one-half of a sample period. It is interesting to note that the inverse relation is also true, Now the RMS value of G(t) (RMS value of integrated pulses) is although in a more limited sense. If a time series with a regular given by repetition rate F is passed through a low pass filter with cut-off RMSIP [2rrFl S( ) 12d (4-10) frequency F/2, the RMS value of the continuous signal at the Uo filter output is exactly equal to the RMS value of the time series. where This is proved in Appendix 5. S(w) = I T(w) I I s(w) I Let us assume a continuous fluctuation noise signal g(t) with a p m s() of random phase arc tan([s()]/R[s()]) where and 2rrF is the angular frequency of the upper limit of the radio spectrum s(w) of random phase 0-arc tan(CI[s(o)]/R[s(w)) where ik video pass band I and R, respectively, denote the imaginary and real parts of s(w). hanging from angular frequency to cyclic frequency we The correlation properties of the noise signal will determine the ha fr t c of an r r to ci r f RMS value per unit band width I s(w) as a function of frequency where Is(w)] denotes the magnitude of the complex valued spectrum function s(w). The m-th term of the time series corre- RM-IP(FMnoise) = J [T(2rf)2kl2df (4-11) sponding to the integrated sample is and for the case of an AM radio link and for the case of an AM radio link anF;(/PfanF) g(t)dt. (4 RMS-IP(AM noise)= [fo I T(2rf) 2k2df]* (4-12) The same time series is obtained as instantaneous samples of the Treating the FM case first we obtain function G(t) taken at the rate F where G(t) = anFf:(l/n)g(T)dr. (4-2) RMS-IP(FM noise) = - (J sin df Thus to evaluate the RMS value of the time series consisting of the 2anF\ irr. 2i integrated pulses it is, by the preceding arguments, only necessary -kI - ) sn- ^ a. (413) to obtain the RMS value of G(t). We may write In most practical work we may assume r> an as in reference (R4). Under these conditions neglect of the trigonometric term under the G(t) =G (t) - G2(t) =G (t) -I(t- ) (4-3) radical will cause less than 10 percent error in the expression. The 1\anF/ result is where nFiri Gr C(l) = anFf g(r)dr RMS-IP(FM noise) = k1 (4-14) t-a(I/anF) With signal of RMS value S this provides exactly the same signalG2(t)=anFfJ g(r)dr to-noise ratio as the low pass filter. [See Eq. (7) in reference (R4) and c is any constant. Now the spectrum S(o) of G(t) is the differ- with fma= F/2. ence of the spectrum Sl(w) of G1(t) and the spectrum S2(w) of G2(t). The AM case gives That is koanF( 1 if S(w) = S1()-St(w). (4-4) RMS-IP (AM noise) ( sin df/ (AM) noise)~St. ^-T f2 anF / Integration of a time function multiplies its spectrum by the kanF\ rr/ansiny Vt factor 1/iw(i'= -1). Thus 2s dy. (4-15) Sl(w)= anFs() N(4-5) ow We recall that J y2 2' If wet again assume r>an then (! sin^Y <CrT/an sinYd X When a time function is delayed by a time 1/anF, its spectrum J sin2 <JO y2 siny 2 is multiplied by the factor exp(- iw/anF). Thus Now S2(o) =S)(w) exp(-) F -~ (4-6) f sin2dy= 0.852

28 M. H. NICHOLS AND L. L. RAUCH so the radical term in the expression is equal to (7/2)i with an (B2) W. R. Bennett, Bell System Tech. J. 20, 199 (1941). error of not more than eight percent. The result is (B3) W. R. Bennett, Bell System Tech. J. 27, 446 (1948). /SnF\ (B4) W. P. Boothroyd and E. M. Creamer, Elec. Eng. 68, 583 RMS-IP(AM noise) =k2 -). (4-16) (1949). (B5) H. S. Black and J. O. Edson, Elec. Eng. 66, 1123 (1947). With a signal of RMS value S this provides exactly the same (B6) Buhler, Freeman, and Saunders, U. S. Air Force (Air Tech. signal-to-noise ratio as the low pass filter [see Eq. (11) in reference Intell.) Tech. Data Digest 13, 11 (August 15, 1948). (R4) with f, x= F/2]. (B7) W. G. Brombacher, Instruments 20, 700 (1947). Using the above procedure and the method developed in refer- (C1) J. C. Coe, Proc. Inst. Radio Engrs. 36, 1404 (1948). ence (R4), it can be proved that the noise reduction obtained by a (C2) E. H. Colpitts and 0. B. Blackwell, Trans. AIEE 40, 205 low pass filter of band width F/2 is the same as the noise reduction (C3) M. S. Corrington, Proc. Inst. Radio Engrs. 33, 878 (1945). obtained by pulse integration for any fluctuation noise spectrum. (C4) M. G. Crosby, Proc. Inst. Radio Engrs. 25, 472 (1937). (C5) R. E. Conover, Instruments 23, 445 (1950). APPENDIX 5 (C6) Chisholm, Buckley, and Farnell, Proc. Inst. Radio Engrs. 39, 36 (1951). RMS VALUE OF A SMOOTHED TIME SERIES (D1) C. A. Dyer, Elec. Eng. 69, 643 (1950). (El) S. B. Elggren, Instruments 18, 2 (1945). Let us assume a time seres occurring in regular time sequence (E2) J. F. Engelberger and H. W. Kretsch, Elec. Eng. 69, 642 at the rate F. We first show that such a time series can always be (1950). the result of taking instantaneous samples of some continuous (F) C. L. Frederick, Elec. Eng. 65 (Supplement) 861 (1946). signal containing no frequency components above F/2. It is clear (F2) C. L. Frederick, Sc. Ep. Stress Analysis Proc. 4 No. 2 that if we do not so restrict the band width of the continuous signal 103 (1947). then there is always a "wide band" continuous signal whose (). H. Gerks, Proc. Inst. Radio Engrs. 37, 1272 (1949). samples give rise to the time series. (G2) S. Goldman, Frequency Analysis, Modulation and Noise Now the spectrum of the sampled signal arising from this wide (McGraw-Hill Book Company, Inc., New York, 1948) band continuous signal will be, according to Eq. (2) of reference Chapter IV (R4), a series of carriers", located at frequencies mF(m = 1, 2, ), 3) W. M. Goodel, Bell System Tech. J. 26, 395 (1947). with AM sidebands above and below each carrier according to the (G4) W. E. Greene, Electronics 21 124 (September, 1947). spectrum of the wideband continuous signal. The sideband com- (G5) Grieg, lauber and Moskowitz, Proc. Inst. Radio Engrs. ponents for each carrier corresponding to a given signal component 35,1251 (1947) have equal amplitudes. A little observation will show that although (H) C M Hathawayand E S Lee Mech Eng 59 653 (1 sideband components may be located much farther from their H E S Lee, Mech. En. 5, (H2) Heeren, Hoeppner, Kauke, Lichtman, and Shifflett, Eleccarrier than F/2 the components within F/2 of each carrier, many 1 (a, 14 and Elecn, 14of which may belong to other carriers, are arranged symetrically Electronics 20, 124 about the carrier in an AM fashion and are exactly the same as the (April, 1947). components located within F/2 of every other carrier. In the light (H3) G. L Hckley, Electronic Eng. 21, 209 (1949). of reference (R4) this means that the sample signal (time series) (H4) P. G. Hel, Inroduction o Mathematical Satistis (John can equally well arise from a restricted band width continuous Wiley and Sons, Inc., New York, 1947) Theorem II, signal whose spectrum is exactly the sideband components within Chapter IV. F/2 of any carrier. (H5) B. D. Holbrook and J. T. Dixon, Bell System Tech. J. 18, Thus we have shown that the time series can be considered as 624 (1939). arising from sampling a continuous signal containing no frequency (H6) A. Hund, Frequency Modulation (McGraw-Hill Book components above F/2. It will be noted that the above argument Company, Inc., New York, 1942). breaks down for wide samples because the corresponding sideband (J1) A. E. Jabitz, Elec. Mfg. 77 (February, 1950). components for different carriers may have different amplitudes. (K1) O. E. Kell, Wireless Eng. 18, 6, 56 (1941). This is because a sequence of wide samples contain much more (K2) L. G. Killian, Electronic Ind. and Electronic Instrumentainformation (lost in the smoothing process) than the time series tion 2, 3 (April, 1948). formed from instantaneous samples. (K3) S. C. Kleene, Proc. Inst. Radio Engrs. 35, 1049 (1947). It is well known(R^ that when a signal containing no com- (K4) M. Kiebert, Aeronautical Conference, London, 1947, page ponents above F/2 is sampled at a rate F, and the samples passed 241 (Royal Aeronautical Society, 1948). through a low pass filter with cutoff F/2, the signal out of the low (K5) E. R. Kretzmer, Proc. Inst. Radio Engrs. 35, 1230 (1947). pass filter is exactly the original signal except for any time delay (L1) V. D. Landon, Proc. Inst. Radio Engrs. 24, 1514 (1936). introduced. Now when we smooth the time series by a low pass (L2) V. D. Landon, RCA Rev. 9 287 (1948). filter with cutoff F/2 the signal out of the filter is exactly the (L3).. Lehan, Electronics 22 90 (August 149) restricted bandwidth signal of the preceeding paragraph whose ( F. G. Logan Electronics 2, 104 (ctobe, 1948). samples give rise to the time series. As pointed out in Appendix 4 the continuous signal giving rise to the time series has exactly the (L5) R. D. Lord, Phil. Mag. 39, 66 (1948). RMS value (standard deviation) of the time series. Therefore the (L6) Leiss, Nitchie, and Underhill, Instruments 20, 709 (1947). smoothed time series, using a low pass filter of cutoff F/2, has (M) L. A. Meacham and E. Peterson, Bell System Tech. J. 27, 1 exactly the RMS value of the time series. If the time series is (1948). smoothed with a low pass filter of cutoff f<F/2 then RMS value (M2) G. H. Melton, Electronics 21, 106 (December, 1948); see of the smoothed signal may be less than that of the time series also Mayo-Wells, Instruments 23, 717 (1950). depending upon the spectral distribution. If this is uniform (white) (M3) J. T. Mengel, Instruments 23, 70 (1950); see also N. R. the RMS value is (2f/F)i times that of the time series. Best, Electronics 23, 82 (August, 1950). (M4) S. T. Meyers, Proc. Inst. Radio Engrs. 34, 256 (1946). Reference List (M5) H. Matheson and M. Eden, Rev. Sci. Instr. 19, 502 (1948). (M6) Moskowitz, Diven, and Feit, Proc. Inst. Radio Engrs. 38, (Al) J. Andresen, Instruments 23, 347 (1950). 1330 (1950). (B1) W. R. Bennett, Bell System Tech. J. 19, 587 (1940). (01) M. O'Day, Elec. Eng. 69, 642 (1950). Is The carriers may or may not be suppressed according to whether there (02) Oliver, Pierce, and Shannon, Proc. Inst. Radio Engrs. 36, ia not or is a DC component in the continuous signal. 1324 (1948).

RADIO TELEMETRY 29 (P1) J. P. Paine, Instruments 20, 30 (1947). (R14) H. C. Roberts, Mechanical Measurements by Electrical (P2) W. H. Pickering, Soc. Exp. Stress Analysis Proc. 4, No. 2, Methods. (The Instruments Publishing Company, Pitts74 (1947). burgh, 1946.) This material is also published in Instru(Rl) Radio Research Laboratory Staff, Harvard University, ments 17, pages 196, 260, 334, 398, 475, 534, 603, 668, 742 Very High Frequency Techniques (McGraw-Hill Book (1944); 18, pages 10, 83, 150, 225, 299, 389, 462, 542, 616, Company, Inc., New York, 1947), Vol. I, page 392. 685, 882 (1945). (R2) W. Ramberg, Elec. Eng. 66, 555 (1947). (S1) H. Schaevitz, Soc. Exp. Stress Analysis Proc. 4, No. 2, 79 (R3) L. L. Rauch, Electronics 20, 114 (February, 1947). (1947); see also W. D. MacGeorge, Instruments 23, 610 (R4) L. L. Rauch, Proc. Inst. Radio Engrs. 35, 1230 (1947). (1950). (R5) Resume of Telemetering Practice Up to 1941. AIEE Com- (S2) R. W. Sears, Bell System Tech. J. 27, 44 (1948). mittee on Automatic Stations and Instruments and (S3) A. M. Skellett, Bell System Tech. J. 23, 190 (1944). Measurements, Trans. AIEE 60, 1411 (1941). (S4) A. M. Skellett, Proc. Inst. Radio Engrs. 36, 1354 (1948). (R6) Rev. Sci. Instr. 16, 158 (1945). (S5) C. K. Stedman, Proc. Inst. Radio Engrs. 36, 36 (1948). (R7) Rev. Sci. Instr. 18, 376 (1947). (S6) C. E. Shannon, Bell System Tech. J. 27, 623 (1948). (R8) Rev. Sci. Instr. 18, 804 (1947). (S7) H. Sostman, Instruments 23, 37 (1950). (R9) Rev. Sci. Instr. 18, 859 (1947). (T1) F. E. Terman, Radio Engineering (McGraw-Hill Book (R10) Rev. Sci. Instr. 19, 373 (1948). Company, New York, 1947), page 770. (Rll) Rev. Sci. Instr. 20, 328 (1949). (W1) D. K. Warner, Instruments 22, 314 (1949). (R12) Rev. Sci. Instr. 20, 626 (1949). (W2) D. E. Weiss, Soc. Exp. Stress Analysis Proc. 4, No. 2, 89 (R13) S. O. Rice, Bell System Tech. J. 24, 46 (1945). (1947). (R5.1) AIEE Report on Telemetering, Supervisory Control and Associated Circuits, Sept. 1948. (R5.2) Proceedings of the joint conference on telemetering sponsored by the AIEE and the National Telemetering Forum, AIEE Special Publication No. S-41, Aug., 1950.

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