Technical Report No. 201 03674-24-T TRIBAND: THE THREE BAND FILTER FOR THE CONTINUING MIMI EXPERIMENT by Norman Hatter Approved by:>< CA.x _ Theodore G. Birdsall for COOLEY ELECTRONICS LABORATORY Department of Electrical Engineering The University of Michigan Ann Arbor, Michigan Contract No. Nonr-1224(36) NR187-200 Office of Naval Research Department of the Navy Washington, D. C. 20360 February 1970 Reproduction in whole or in part is permitted for any purpose of the U. S. Government

ABSTRACT An experiment was conducted as part of the continuing study of sound propagation in the Straits of Florida. A 420-Hz continuous wave (CW) signal was transmitted, received at the 7-mile hydrophone, and processed by the Linc-8 on-line digital processor. The processing yielded the magnitude and phase of the reception in a 1/16-Hz band, the magnitude of the reception in a 1-Hz band but excluding the 1/16-Hz band, and the magnitude of the reception in a 16-Hz band that excluded the 1-Hz band. All bands were centered at 420 Hz. The purposes of the experiment were to verify the possibility of such a three-band analysis and to obtain "typical" relative power ratios to aid in the design of analog triband phase coherent demodulation. iii

ACKNOWLEDGE ME NTS The author wishes to thank those people who made contributions that were instrumental in the conception, development, and execution of this experiment. The work performed by the members of the Acoustics Group of the Institute of Marine Sciences (IMS), in particular, the assistance given by R. Dann, was most appreciated. In the Stochastic Signal Processing Group, Cooley Electronics Laboratory (CEL), The University of Michigan, Dr. T. G. Birdsall outlined the experiment and the data acquisition methods. K. Metzger and G. Cederquist offered helpful suggestions on data processing and analysis. M. Baker, B. Barton, J. Nepiuk, and J. Capps plotted much of the initial data and filter transfer graphs. The guidance of Dr. T. G. Birdsall through all phases of this experiment and his excellent preparation of Appendix A were invaluable. Mrs. A. Fulmer was especially helpful in the typing and preparation of this report. The careful preparation of many of the illustrations was the work of the CEL Reports Office. Finally, the author wishes to thank the sponsor without whose cheerful support this project could not have been completed. iv

TABLE OF CONTENTS Page ABSTRACT iii ACKNOWLEDGEMENT S iv LIST OF ILLUSTRATIONS vi CHAPTER 1: INTRODUCTION 1 1.1 MIMI Description 1 1. 2 Proposed Model 3 CHAPTER II: BACKGROUND AND PURPOSE 7 2.1 The Experiment 7 2.2 Bandpass Filter Implementation 9 2.3 Analog Filters 11 2.4 Digital Block Averaging 15 2.5 The Digital Process 22 CHAPTER III: RESULTS 30 3.1 Triband graphical results 30 3.2 Triband correlation results 31 3.3 "Phase Jumps" in Triband 32 CHAPTER IV: CONCLUSION 33 APPENDIX A: ON THE QUADRATIC CONTENT TRANSFER FUNCTION OF A NONLINEAR PROCESSOR 35 APPENDIX B: INDIVIDUAL POWER TRANSFER CHARACTERISTIC PLOTS 48 APPENDIX C: TRIBAND GRAPHICAL RESULTS 57 APPENDIX D: TRIBAND CORRELATION RESULTS 82 REFERENCES 87 DISTRIBUTION LIST 88 v

LIST OF ILLUSTRATIONS Figure Title Page 1 (a) Straits of Florida, Miami to Bimini 2 (b) Bottom Profile, Fowey Rocks to Bimini 2 2 Triband experimental system 6 3 Three band filter 9 4 One bandpass filter implementation 10 5 Another bandpass filter implementation 10 6 Analog filter impulse response 11 7 High-pass filter power transfer chart 14 8 Analog filter impulse responses 16 9 Average high-pass power transfer characteristic 19 10 Bandpass power transfer characteristic 21 11 Partial digital process 22 12 Summation impulses 23 13 Three band filter power transfer characteristic 26 14 Complete digital process 29 15 Filter diagram 36 16 Linear averager 38 17 Triband post demodulation processing 44 18 Individual power transfer characteristic, k=0,15 49 vi

LIST OF ILLUSTRATIONS (Cont.) Figure Title Page 19 Individual power transfer characteristic, k = 1,14 50 20 Individual power transfer characteristic, k=2,13 51 21 Individual power transfer characteristic, k =3,12 52 22 Individual power transfer characteristic, k=4,11 53 23 Individual power transfer characteristic, k=5,10 54 24 Individual power transfer characteristic, k=6,9 55 25 Individual power transfer characteristic, k= 7,8 56 vii

1. INTRODUCTION 1.1 MIMI Description The project MIMI is a joint experimental effort of the Acoustics Group of The Institute of Marine Sciences (IMS), University of Miami, (MIMI-A), and the Stochastic Signal Processing Group, Cooley Electronics Laboratory (CEL), University of Michigan, (MIMI-C). The nickname "MIMI" was generated by concatenating the first two letters of both Miami and Michigan. The acoustic and environmental test facility is maintained and operated by MIMI-A, which is also responsible for the majority of the environmental studies and propagation studies. MIMI-C is responsible for the development of signal processing techniques to improve the reliability and relevance of the experimental propagation data. The signal source is a flextensional transducer mounted at the focus of a 24 ft compliant-tube parabolic reflector. The whole assembly is located off Fowey Rocks at a depth of 85 ft (Ref. 1). The experimental channel used in this study is that portion of the Straits of Florida approximately located between Fowey Rocks and the "seven-mile" hydrophone. The relevant features of the channel are illustrated in Fig. 1. The bottom profile shows a 350 meter deep shelf just beyond the hydrophone. In addition to added interference - 1

25~:. Depth in fathoms 25.*:y< ^ VIRGINIA KEY 0 /t' *f4d |,',,,o f 41A T L A N T/AN I C t2 1 97 *: 12 7 Qj^~~~ 70 N 332. FO EY ROCKS / 4i 481, CAT CAY 150. \. IMII 73, 213 240 / 39'04 0 OCEAN 46. 91 2'.'zo r' jy 142 t.12 / I. POWER SIGNAL CABLES0 10' 800 50' 40' 30' 20' 10' Fig. 1 (a) Straits of Florida, Miami to Bimini 80e00' 795Od 79040' 7930 7920' W.,_ 400 \ / \*/142 800 (VERTICAL SCALE 37 HOR I ONTAL) 0 10 20 30 40N. ILES I'* I I (ONE TO ONE SCALE) Fig. 1 (b) Bottom Profile, Fowey Rocks to Bimini LOCATION OF OCEANRAPHIC DATA STATIONS 1T 2? ^30^ 3 4 5 6 1 71 200- / uj400 ^ / ~ 600e. / -o 800(ONE TO ONE SCALE)

from biological noise, surface related noise, and shipping noise, the signal is distorted by the slowly changing multipath structure and the rapidly changing instantaneous position of the surface. A quantitative measurement of the effects of this last, the surface waves, is one of the purposes of the triband processing. The data acquisition devices consist of the hydrophone, seven miles of underwater cable and its amplifiers, a telephone line from Fowey Rocks to MIMI-A and the terminal amplifiers there, and then in parallel, amplifiers and filters to a phase coherent demodulator, Sanborn strip chart recorders, and two on-line Linc-8 digital computers. One digital computer was used as the primary processing device for this experiment. Figure 2 shows the overall system configuration. 1. 2 Proposed Model From the earliest MIMI studies, and continually on all studies at all phones, the effect of the surface waves as a source of modulation has been evident. Power spectra of continuous wave (CW) amplitude fluctuations, carrier phase fluctuations, and local wave height all coincide in shape, although differing in magnitude. This is a wellknown phenomena, well understood in-the-small (one surface interaction, small ensonified area) but not often quantitatively measured or modeled to the extent necessary for prediction. 3

Examination of Sanborn strip chart records of the received CW amplitude and phase indicate that the major effect is an amplitude modulation (AM), with some minor phase modulation (PM). Both AM and small angle PM primarily produce first order sidebands. The wave periods at MIMI have 2 second to 10 second periods, giving rise to sidebands of 0.1 Hz to 0. 5 Hz on either side of every transmitted spectral line. Most MIMI processing has used narrower filters for CW or narrow tooth comb filters for sequence transmissions to eliminate this modulation effect from the analysis. Therefore we have been confident that this surface-wavemodulation is present, but have no quantitative measurement to establish its magnitude or to study its behavior under changing conditions. The primary purpose of triband analysis is to obtain such quantitative measurements. Continuing studies of the MIMI 7-mile and 42-mile channels almost invariably measure two types of carrier power fluctuation sharp,deep fades typical of multipath destructive phase interference with recurrences of the order of 15 to 60 minutes, and gross level changes in the maximum "between-fade" levels with changes spread either over months or occasionally with rapid transition in a few hours. The second purpose of triband analysis is aimed at the type of fade with the 15 to 60 minute recurrence. Are these fades accompanied by an increase in the power in the surface-wave sideband region ~ 0. 5 Hz off 4

carrier? If this occurs, the implication would be that the carrier was being angle modulated by the waves present. It is well known that for the case of pure angle modulation, the total power remains constant; it is merely exchanged between the carrier and its modulation sidebands. 5

Ultrastable Frequency Reference Frequency Synthesizer at 1680 Hz Transducer Hydrophone Oscillator ]JLine Fowey _ - ile Power "7-mile" Amp at 420 Hz J rI Amp Channel Amp Sync Other Telephone Circuit Equipment Lines Synchronizing Pulses Laboratory Terminal Fowey Marine cable Amp, Filter Amp Amp Linc - 8 Linc-8 Digital Processor Magnetic Tape Fig. 2. Triband experimental system

2. BACKGROUND AND PURPOSE In this experiment, the signal from the channel is separated into carrier and sideband components. The sidebands are further divided into a narrow sideband (nsb) and a wide sideband (wsb). The power in each band is calculated and averaged over a fixed time period. The correlation coefficient for these samples was calculated and examined. If the proposed model is correct, a strong negative correlation between the carrier power and the sideband power is expected. The use of a three-band filter gives rise to the nickname "TRIBAND". 2.1 The Experiment The experiment called for a 420-Hz continuous wave signal to be transmitted through the channel. The signal would then be received and digitally processed. The MIMI project is unique in that measurements are made between two fixed sites, thus eliminating the necessity of correcting for drifting sites. The transmitter consists of precision oscillator (1 part in 1010) from which the 1680-Hz clock frequency is derived. The 1680 Hz is further divided to 420 Hz which is then transmitted by cable to the amplifiers at Fowey Rocks lighthouse. The amplifier output is then coupled, by cable, to the transducer. The piezo-electric hydrophone receives the signal which is then conducted to IMS via cable. At IMS the receiver signal is amplified to a range of 7

less than ~ 1V in order that the input to the fixed bandpass filter and the A/D converter is not exceeded. From there, the signal is passed through a passive, fixed filter with a 120-Hz passband centered at 420 Hz and sampled by the A/D converter for subsequent digital processing. After processing,the digital data is written onto magnetic tape for post-processing. The data is also typed out on a teletype for correlation with the taped data. Our primary concern will be with the signal after it has been received at IMS. A synchronizing signal is provided to ensure that phase coherency is maintained. The 1680 Hz is also used to sample the signal waveform. Ideally, the 420-Hz signal is sampled four times per cycle which is more than adequate to recover all of the information and is exactly four times the carrier frequency to facilitate demodulation. The computer then performs the filtering in accordance with the description in Section 2.5. 8

2. 2 Bandpass Filter Implementation The concept of the filters for the experiment is sketched in Fig. 3. Lr 1 Iflfl < f | e[ ul^^y (t) HLP(f) 0 elsewhere x(t) —- BP"1 y2(t) H (f) 1| U 1-Cf1 0O elsewhere fl f f-BP --- 1 f< < lfl<f x 2A -- y3(t) H (f) I - L2' y3( -fBP2 0 elsewhere f2 Fig. 3. Three band filter The implementation of the bandpass filters posed the most difficult problem. The bandpass filters might be realized by using the following scheme:

x(t) LP HP y(t) f2 f. Fig. 4. One bandpass filter implementation That is, a low pass filter and a high pass filter are cascaded to form the bandpass filter (Fig. 4). The same effect could be achieved by combining two low pass filters as in Fig. 5. I i - x - f I LP 2 Fig. 5. Another bandpass filter implementation The output of the narrower filter is subtracted from the output of the wider filter forming a bandpass filter. For ease of digital implementation, this is the method that was chosen. 10

2. 3 Analog Filters Consider the analog filter which is analogous to the digital process (Fig. 6). The proposed filter would have impulse response: h(t,T) = 1/T It < T/2 (1) 0 Itl > T/2 h(t, r) 1/z - T/2 7/2 Fig. 6. Analog filter impulse response This filter may be realized if sufficient delay is incorporated. The transfer function is H(f, 7) = f h(t, T) e-Jt dt -x0 T = 1 f2 e jct dt _T T 2 where j = m co = 2 f 11

2 r/2 H (f, ) - J/ cos ot dt 0 2 T/2 -= 2- [sin ct] CT 0 2 2 T f2irfT [sin 2 ] sin v f T = = sinc (f 7) (2) 7TfT If two low pass filters are combined as illustrated in Fig. 5, one having m times the averaging time of the other, the transfer function for the combination becomes H (f,T) = J h (t T) e t dt c c =sinc (fT) - sinc (fmT) (3) where hc(t T) h1(t, 7)- h2(t, T) This function can be factored to yield the corresponding high pass and low pass filters as in Fig. 4. H (f, T) = sinc (fT)- sinc (fmT) H (f T) =sin 17f sin Tf m T =c 1rfT ~rfmT (4) sini ifT [ sinlrmfTl = H = snfiT [1 - m sin 7fT HL (f, T) HH(f, m ) 12

The power transfer function of the high pass filter is: HH2 (f, mT)= - sinwmfT]2 Hp L_ m sin fTj ( The important characteristics of the high pass filter are: First, H (f) = 0 m = in 1 (6) HlP ~ ~ m sin lrf or sin TrmfT = m sin rf T (7) which only occurs when fT is an integer. In particular,at f = 0, the power transfer is zero. H2p(O) = 0 (8) Second, HHP(f, m ) = 1 -> sin 7mf T/m sin rf T = 0 or sinTrmfT = 0 => mrmfT = k7T -=> f = k/mT Hence, HHp(k/mT)= 1, k=l,2,..., m-1 (9) For T = 1/16 and m = 16, the 3 dBbandwidth of the reject region about dc is approximately 1.4 Hz. 13

sin rf f 16 sin -) [ 1 - sin- f 2 1.0 sin 7f 7nf 16 sin (~-6) 0.5 Hz 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 Fig. 7. High-pass filter power transfer chart

The "overshoot" of the high pass filter for m = 16 is approximately 47 percent and occurs at a frequency of about 1. 5 Hz (Fig. 7). 2.4 Digital Block Averaging The objective is to obtain a bandpass filter by differencing two low pass filters. For our processing, the averaging time of the digital narrow band low pass filter was 16 times the averaging time of the digital wide band low pass filter. This means that for each value out of the narrow filter, there were 16 values out of the wide filter. That is, there was one value from each of 16 wide filters which were selected sequentially in time during the averaging period of the narrow filter. Although this digital situation is similar to the analog just considered, the processing is not time invariant. The output of the narrow filter will have to be subtracted from each of the outputs of the 16 wide filters. This method of processing is called a "block averaging" or a "synchronous, cyclostationary" technique. The analog impulse responses are illustrated in Fig. 8. These impulse responses are not realizable, but may be made so by allowing sufficient delay. The required delays are given in Eq. 10, where: (a) 1/2 T is the delay necessary to make each wide filter realizable, (b) k T is the delay necessary to pick the appropriate output for differencing, and 15

h(t, m T) 1/16Tt t=0 hk(t, T) 1/T [kY=O ___l/'''- ___ _ k=O k=l k=15 i-T - 1.5 T t = 0 14.5 T 15.5 T Fig. 8. Analog filter impulse responses (c) 8 T is the delay necessary to make the narrow filter realizable. hk(T) = h[t- (k+)T;T] - h(t- 8T; 16 T); k = 0,1,..., 15 (10) The transfer function for Eq. 10 is: Hk(f) = exp[-j27r(k+~)fT] sinc(fT) - exp(-j l67rfr) sinc (16fT) (11) k Lssinin6(rfT j where Hk(f) has been factored into a low pass and high pass product. The power transfer characteristic of the low pass filter is the familiar sinc2(fT) function. The high-pass filter power transfer characteristic is a function of the delay, k. 16

HHP k(f) 2 exp[j; (15- 2k) f ] - in 6 f 7) (12) 16 sin(7Tf () Recall: IHI2 = H H* (H complex) (13) and ej ^2 = (ej0- )(e-j- ) 1+ 2 _ (ej +e- 3) 1+ 2 - 2p CoS a (14) Therefore, a more convenient form of the high pass power transfer characteristic is the real equation 2 sin(ll 6fT) 2 sin(6fT) =, 1 ~ rL ] 2 sin((l 6f T) |Hp ktfl = 1 + 6sn(i) - 2 l6sin(f) cos (15-2k) TfT HP1 k 6sin~vf r 16sin(-f T) k = 0,1,..., 15 (15) The individual power transfer characteristics for k = 0, 1,.., 15 have been plotted and are given in Appendix B. It is evident that each of them varies about the desired rectangular pass band. However, our processing calls for a fairly rectangular pass band with variations reduced to a minimum. In our processing, we are interested in the power in the band. We estimate the power by averaging the magnitude squared of the output 17

of 16 outputs. Hence, we look at the average of the individual power transfer characteristics which is averaged over the 16 delays in the block averaging process.* Accordingly, the bandpass power transfer function is the average of the individual bandpass power transfer functions that are a function of the delay, k. Using this approach, we see from Eq. 11, that only the high pass filter is a function of the delay, k. The low-pass filter is merely the sinc2(fT), unconditional upon k. From Eq. 15, it is noted that the third term is the only one which is affected by k. Accordingly, we shall average over the cosine term. The average value of a set of cosines at uniformly spaced frequencies and symmetric about zero is 16 cos ((15-2k) f7 = sin6fT (16) ok=o 16 sin irf7 From which, HHP(f)2 = 6 HBP K(f)2= 1 - (f (17) k=0 P' m sinif7T This average high-pass power transfer characteristic is plotted in Fig. 7 and also in Fig. 9. *See Appendix A for development. 18

1.00. 9 0.8 - 0.7 0. 6 - 0.5 - 0.4 - 0.3 - 0.2 - 0.1 - 1 2 3 4 Hz.45 Fig. 9. Average high-pass power M = 16 Transfer characteristic

To obtain the bandpass power transfer characteristic we use Eq. 17 and Eq. 12. iHBP(f) 2 = tHLp(f) I-HHp(f) 2 (18) f2 sin7rfT\2 F sin 7Tmf.T\ HBP(f) ( mi ) [1 - Im sin nf) 1 (19) HBp(f)l2 = sinc2(f ) - sinc2(mfT) (20) Equation 20 is the bandpass power transfer characteristic of interest and turns out to be simply the difference of two sinc2 functions which is the power transfer function of the bandpass filters described in Section 2. Figure 10 is a plot of the bandpass power transfer characteristic. 20

-4 + (D C CD ) iD CD CD D (D ~ CD C ) D CD CDC.D: I C) C) CD CD CD O O l rD C O CD (3 k C. D CD C.) C) CD'3 D C CD 4 — — D CD -~ D — D ~ D (:CV C-) + + + + + + + - + + + + + + + + + + + + + + + + + + + + + + + + + + + + ++- + + + + + + + I I I I I I I I I I I I L IJ W J L l- J LiJ W W W L Ll iJ LA J LLJ 1x J WJt LW L dXJW LO J LL W W LJ d lJ Ldl J J1 WJ WLW LLJ i X J I- L lJ L& Ui W i I xJ IJ l IJ x J l U l 1J I IrL J jx lJ II *A BW W)- CA N3 CD N Cb c ku n I CA A cG l 4 M CA<- (lOC r C K W -qV Dn r -- * o P ) -+t r- Cvo (C tO (0 (0 Q n V) WI N(/ C n n C ru LrBn Ln LC Cr r- LCc cN M r - 0o C D1 c V 4) D f o C] () N r r- f- CD 1 W r- if l-n - c M ) L r T 2 * l W- N C' - L ( - D -7 M O W M V) t tfl'll C L n C-3 rc- CD N) CA -7j r- (A 7 C -( -L Q Cn (A -T W IT N C - L CIO;3T u', - to CO C3 kn -- F3) Pe r 3 W e) ( -( ~[:C!i n I M) r) C) m-7 N'T ~q C- O m V., -v N c - 0 -I o V) w m6P) - to ln r- C> 6 w n Nj 6 t,- tn r, L m kn -~ cui cD oo kn T Pt C ci, r- v,, kn r- no -oK pr — v as -v o I -U' Ca CrA CA 4A a sA CA Mr o CD rcc Cr cc r 4- r- r- r v-( (1) ( k rn ur U-N L%, V N - -, 14 ). 4 ) FO PO ) CQ C( N C\] I'M — C \, A r- C UN'L, 14)?-) N\ -O - CA) c;4 CC (C 4 * I 0. 0 0 0 0 0 0 0 0 0 0 O O O 0 0 0 0*00 O O 0 0 O O -t i' ~~~~~~~~6 sin,,1~~~si sin sin y 1.0+in J~~~~~~~~~~~~. 20 3. I0 4. 0 5.0 10#2 Fig. 10. Bandpass power transfer characteristic

2.5 The Digital Process The signal is digitally demodulated and then summed to obtain the desired outputs. Figure 11 is a block diagram of the process. z (t) 16 + Demod. Store -Diff ---- ZA(T) 1/16 1. Z ) ——' --— TC Fig. 11. Partial digital process The signal is sampled at the 1680 Hz clock frequency. Prior to sampling, the analog signal is passed through an analog filter with 22

a 160 Hz bandpass centered at 420 Hz. Hence, an alias is avoided since signal components of 840 Hz and above are negligible. The demodulation process essentially shifts the band of interest down to dc. The transfer function (Ref. 2) of the demodulation process is H(f) = je-J2T sin47f~T (25a) cos vrfT IH(f)l = sin 47f T (25b) Icos rf TTt T = 1/1680 sec The output rate from the demodulation process is 210 complex values/ sec. The summation may be viewed as a filter whose impulse response is a string of impulse functions (Fig. 12). 0 I I 1... *TT. I)t 0 T 2T 31 4T (N-1)T T = 1/210 sec Fig. 12. Summation impulses 23

As a digital filter, the response is: N-1 h(t) = v 5(t- nT) (26) n=O The transfer function is: (N- I)T H(f)= S 5 &(t - nT) e-2ft dt n=O (N-1i) (N- l)T -= S 6(t- nT) e j2ft dt n=O 0 N-1 = e j2n (27) n=O Recall: n+1 n i-x ( 1 + x + x2 +.... + x - x x < 1 (28) Therefore, 1 e- j27rfNT H(f) - e -j7ifNT (ej7fNT - e jrfNT) = -jTrfT e fT (e gfT - ej fT) 24

e-j rf(N-1)T sin (rfNT) (29) sin (rfT) IH(f)l = sin(yfNT)l (30) I sin(TffT) I where: N = 16 for the 1st filter -> NT - 0.08 sec N = 256 for the 2nd filter -> NT - 1.22 sec N = 4096 for the 3rd filter => NT _ 19.5 sec These numbers have step ratios of 16 and were chosen so that the surface wave periods of approximately 2 to 10 seconds fall between NT =1.22 sec and NT =19.5 sec. From Eq. 30 and Fig. 11 it can be seen that the resulting averaged difference power transfer characteristics are IH3(f) 12 sin 4096 sin fT (31) 3 409 6 sin - fT_ sinr256 fT 2 sin 4096 6fT2 2 1H2(f)1 = L2256 sin 7TfTJ [4096 sin rfT (32) Hl(f)12 = 2 sinl16fT2 F sin256vfT12 I1 6L 216n i fT 256sin ifT (33) These are plotted in Fig. 13. 25

1.0 1H3 (f)12 1(f)2 0.9 \ 1H \\) o 0.7o- I M 2 0.8 -I I H / I 0.7 1 I \\./ 0.5 / 0. 6 0.4 / 0.3 / 0. 2 0.1l 0 Of 0.1 0.2 0.3 f 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 0.023 0.364 Hz > Fig. 13. Three band filter power transfer characteristic

H3(f) has a pass band of approximately 50 MHz and is thought to contain primarily carrier energy. H2(f) is thought to contain both surface modulated energy and some local noise. H (f) is thought to contain primarily local noise energy. Notice that the transfer characteristics are periodic in 210 Hz. However, this does not become an important factor since the analog input filter has removed all signals 210 Hz away from the carrier Figure 14 illustrates the complete digital process. It is understood that the so-called "y" components out of the demodulator go through a process which is identical to that shown for the "x" components. Samples are taken for 19-53/105 seconds which yields 4096 complex values from the demodulator. These values are processed as follows: 0 < m < 16, 0 < < 256, 0<k< 4096 162+15 x1() = z0(k) (34) k=1 61 16m+15 x2(m)= z1() (35) f =16m 15 x3 = E z2(m) (36) m=0 27

x1() = x1()- 2- X2 16 (37) where 16 = integer part of 2/16 -4 x2(m) = X2(m) - 2 X3 (38) 255 1 =2 (l( (39) 15 X2 = m (x(m)2 (40) P = x +Y1 (41)! 1 1 =2 X2 + 2 (42) P3 = (x3)2 + 3 ((43) At this point in the processing, the power estimates P i = 1, 2, 3 are written onto magnetic tape for further processing. 28

z (t[ 3g'_p3 SStore Sum 2 mp 2-4 J r Store:D I~ 2_lIempl *~l_.ff.~.Y2 3 x tn —-- 1y3 Fig. 14. Compete digital process Fig. 14. Complete digital process

3. RESULTS This chapter describes the results obtained by the threefilter analysis, summarizes the analysis processes, and discusses an interpretation of these results. 3.1 TRIBAND Graphical Results In Appendix C the plots of the processed data are presented. Data are presented in frames of approximately seven minutes length; hence, each page represents about two hours of data. Frame #1 started at 1600 hrs., 3 October 1969. The P. (i = 1, 2, 3) which were stored on magnetic tape were post-processed by a computer program which yielded the plots indicated. The program gives the output in decibels (relative) which is what is actually shown. The scale ranged from a minimum of 10 dB to a maximum of about 68 dB. This range was chosen because the calculated powers never exceeded these limits. In these plots, the following correspondence is used: (1) P P (N) (2) P P(I) (3) P3 - P(C) Since the phenomena of interest are the relative power levels, the fade occurrences, and the correlation between the three powers, the actual power level is not calculated exactly. 30

results indicate that there are periods of both strong negative and strong positive correlation over each of the time periods used. 3.3 "Phase Jumps" in TRIBAND The graphical data for the power estimates indicate a strange phenomenon occurring at random intervals. These are the abrupt changes in carrier phase associated with a change in each of the estimated power levels. P1 and P2 both increase whenever the phase changes while P3 (the estimate of the carrier power) decreases. There appear to be spurious pulses getting into the sample circuitry and causing 90~ (or some multiple of 90~) phase jumps during one sample period. These spurious pulses are thought to be caused by a radar transmitter located in the nearby ESSA laboratory. 32

The phase information for the carrier is given below the three power level plots. The phase angle is expressed as being between -180~ and +180~ with only -180~ being indicated on the plot. The +180~ value is understood to be equivalent to the -180~ value. 3. 2 TRIBAND Correlation Results The correlation coefficients in power (not in dB) for the three bands was calculated. The relationship used was N 3 (xi- x) (i- y) i=1 R xy N N _ 2 [3 (x^. - )Z (- -y)2 i=l 1 il i i=1 where R is the correlation coefficient between the sample points xy {x} and {y}. Also, N X N. xi The results are given in Appendix D. The correlation coefficient was calculated for periods of about 28 minutes and 63 minutes. (That is; N = 56 and N = 126 with the sample points occurring at 30 second intervals.) Since this is a nonstationary situation, the correlation coefficient must be viewed as a nonstationary statistic. The calculation 31

4. CONCLUSION The initial objectives were met, in that the digital three-band filter was implemented and used to obtain the relative power levels desired. The stability of the phase was again displayed as was evident on previous MIMI CW experiments. This fact tends to establish the validity of the processing. The carrier power varied from over 60 relative dB (rdB) to about 30 rdB (which occurred during deep fades). This also agrees with the fade situation previously experienced. The local noise level was fairly constant (background noise) with some bursts which may be attributed to biological noise or man-made noise (e.g., shipping). The incoherent power level appeared to be relatively stable, again with the bursts which occur in the local noise band. As expected, the correlation between the local noise band and the incoherent band is, in general, strongly positive. An interesting observation is that the correlation between the noise band and the coherent band is highly negative on the short time (28 min ) basis, and negative to a lesser degree on the longer time calculations. This tends to indicate the presence of higher frequency (> 1 Hz) modulation components which are angle modulating the carrier. To make this definitely conclusive, however, more studies must be carried out. 33

The digital process described in this report was intended to be a predecessor of an analog process that is to run continuously over a long period of time. When the results of the analog processing are known, the validity of the types and amount of modulation present may be more firmly established. 34

Appendix A ON THE QUADRATIC CONTENT TRANSFER FUNCTION OF A NONLINEAR PROCESSOR 35

ON THE QUADRATIC CONTENT TRANSFER FUNCTION OF A NONLINEAR PROCESSOR* A. 1 Background Consider any time invariant linear filter situation where "the power or energy spectrum" of the input has meaning (Fig. 15). For a steady-state deterministic process, one means a time average; for L2 deterministic process, one means a time integral; and for a wide sense stationary random process (real or complex), one means the Fourier transform of the autocorrelation. x(t) h(r) -^ — ~ Filter x(t) H(f) Fig. 15. Filter diagram One common property of the power or energy spectrum for all these diverse situations is that commonly called Parseval's Theorem. 3C Ave [x2(t)] = f Px(f) df (1) -3C where P (f) is the appropriately defined power or energy spectrum x for whatever type of variable x is, and the definition of "Average" 36 * Written by Dr. Theodore G. Birdsall

is the corresponding appropriate time or ensemble average. A. 1.1 Quadratic Content Transfer Function The power transfer function of a linear time-invariant filter is Power Transfer Function = IH(f)12 (2) where, loosely, H(f) = F{impulse response h(T)} = 72{h(r) at Re s = 01 One can relate the average squared output of a linear filter to the input power or energy spectrum and the filter power transfer function by P (f) = P,(f) IH(f)12 (3) x and D0 Ave[x2] = f P, (f) IH(f)12 df (4) -x x Equation 4 can be used to define a transfer function for both linear and nonlinear processing. Let x be the input to a processor and y be the output. We shall say T(f Ix- y) is the Quadratic Content transfer function iff 37

xC Ave [x2] = f P (f) T(fIx- x) df (5) -cX -x0 A. 1.2 Quadratic Content Transfer Function of an Average Consider a finite number of filter outputs and their simple average as diagrammed in Fig. 16. H —- x I (t) I H1(f)1 I(t) M xM(t) (6)l H (f) 1 A Fig. 16. Linear averager iM x(t) - H2) (6) Because x-x-x is a linear processor, we may work directly with the usual transfer function, and then find its magnitude squared. H(f) M Hk(f) 38

T(flx- x) = - Z Hx(f) (7) Let us not bother to try to simplify Eq. 7. A. 2 RMS Averages A. 2. 1 Quadratic Content Transfer Function of an RMS Averager The first nonlinear processor to be analyzed begins like the simple averager of Fig. 16, with multiple parallel filters. However, instead of the simple average consider the root-mean-square value of the xk(t).: M r(t) = x(t) (8) k=1 Here we may not use the usual transfer function, but reason as follows: 2 M 2 Ave[r] = AveM Xk (9a) k=l The average of the sum is the sum of the averages. M Ave[r2] = -M Ave[xk2] (9b) Mk=l But 39

30 Ave [xk2] = P(f) Hk(f2 df (4) -3C0 So M xC Ave[r2] = M P (f) IHk(f)l df (9c) k=1 -c k x c M Ave[r2] = f P(f) - I Hk(f)l2 df (9d) -X k=l Thus M __z ~ I~k~f)12 T(flx-r) = m r IHH(f) (10) k=1 A.2.2 Quadratic Content Transfer Function of the RMS About the Average The second nonlinear processor again begins like the previous one, with x(t) filtered to yield the set {xk(t)}. Equation 6 still defines x(t). However, let s(t) be 2/M 2 s(t): - E (t) - Ix(t) (1) s2 = (Xk, 2xxk + xk) (12a) 2 2 2- (^ 1 ) X2 (12b) 40

s2 r2- 2xx+x2 = r - x2 (12c) s2(t) = rZ(t)-x2(t) (12d) Again using the linearity of average Ave[s2(t)] = Ave[r2(t)] - Ave [x2(t)] (13) and the linearity of the integral over frequency yields T(flx- s) = T(flx- r) - T(flx-x) (14) Gathering together (7) and (10) yields T(flx- s) = lHk(f)12 - | H(f) 2 (15) A. 3 Delay Lines and Averages A. 3. 1 General Delays In this section we shall consider the case when the parallel filters are pure delay functions. -j2rfTk hk(T) = 6(T- Tk) Hk(f) = e (16) M -j27rfTz 2 T(flx-.x) = e (17) k=l 41

M -j2rf7Tk 2 T(flx- r) =- - = 1 (18) M k=l T(f x- s) = 1- T(flx-x) (19) Apparently the rms averager, (18), is the only nice result. A. 3.2 Uniformly Spaced Delays Let us consider Tk = k + 70 (20) The corresponding filters are realizable iff T7 = A+ T > 0. From experience we learn to factor the exponent -j27rf(kA+ T7) = -jrf(MA+ A+ 27T) - j7Tf(2k- - M) a (21) M - k1 Hk(f) exp (-I7f(MA+A+2TO)) 1 M M k exp(-jTf(2k- 1- M) ) (22) The sum is the sum of a finite geometric series, with ratio between terms of exp(-j7rf2zA). Its sum is M e- jrf(1 - M)A e- jf(M+l)A J exp( —-) (23a) k=l 1- e 42

Factoring out e-jA from every term e-j7f(- M)A - j7fMA -7Tf A e -7TfA (23b) e - e sin rM f (23c) (23c) sin ir f A Returning to Eq. 22, 1 sin r M f A M 2 Hk(f) = exp (- jf(M A+A+ +T)) M sin 7f A (24) M k= M sin f A The first factor represents the average delay of r0 +.5(M+1);and has unity magnitude. The second factor is real; it is the periodic analog of the sine function sinc(fT) = in fT (25),rfT The rest is a quick summary T(flx-sx) = [sin (26) M sin 7Tf J T(flx-r) = 1 (27) T(flx s) = 1- [sinlMf2 (28) 43

A. 4 Analog Triband Using Uniform Delay The subprograms in the digital triband processor use all three kinds of average discussed above (simple, rms, and standard deviation) and also use analog filtering between the raw inputs and the computer, and a demodulation process through synchronous sampling. In this section I should like to consider an analog analogy to that processing that occurs after the input filtering and demodulation. We know that these yield a complex signal that is physically limited to low frequencies, and that only values at discrete instants of time are available because of the sampling. In this analogy I shall suppress these features until late in the analysis. The processing is block diagrammed in Fig. 17. Average — SQ --- P Average z StdDev SQ B —- P z (t) RMS a Std Dev RMS SQ P A Fig. 17. Triband post demodulation processing 44

What is desired is the Quadratic Content Transfer Characteristics between z(t) and a(t), b(t), and c(t). If the input power (energy) spectrum P (f) is known, then the Quadratic Content Transfers could be used to obtain Ave [PA] Ave [P], and Ave [PC] The first average and standard deviation processors use M1 values each, and the time separation is T1 sin M1 T f\2 T(f lz-z) = M sin T f (29) /sin r M T f\2 T(flz-s) = i- M1 sinT ) (30) The second layer of processors use M2 values, and the time separation is T2 = M1 T /sin MT M2MT f 2 T(f z-c) = M2 sin MT1 f (31) _2 2 /sin M MM2T1 f\ T(flz-b) = 1 - M sin7 MT1 f (32) M sin ff M I TI f T(fls-a) = 1 (33) The Quadratic Content transfer function of a cascade of these processors is the product of the individual Quadratic Content transfer functions. 45

Hence T(flz- c) = T(flz-z) T(flz — c) (34a) Msin fs M M2 T f \2 T(flz — c) =MM2 sin Tf (34b) T(flz-b) = T(flz-z) T(flz-b) (35a) sin r M1T1 f 2 sin M1M2T f 2 T(fiz —b) = M sin T1 sln f (35b) T(flz-.a) = T(flz-s) T(fls —a) (36a) /sin r MIT f\2 T(flz-a) = 1- M1 sin T f) (36b) Because the sum of these three transfer functions is unity T(flz-a)+ T(flz —b)+ T(flz- c) = 1 (37) we call these three "complementary," that is, "all the input power is split, and gets through so none is lost or reflected." Equations 34, 35, and 36 are the basic equations used in understanding the special features of TRIBAND. They are repeated below 8 t 105 for M1 = M2 = 16 and T1 = 1. Let f1 = = 13.125 Hz 46

(sin r 256 f/f\2 (34c) ) 256 sin rT f/f ( fI b) 16 sin ff f/f 256 sin f f/f) (35c /sin 16f/f \2 T(f lIz-a) = - 6 sin f/f (36c) All of these transfer functions are periodic, with period 13.125 Hz. The carrier band, "C band," is centered at 0 Hz and has first zeros at. 051+ Hz. The first sideband, "B band," first nears unity transfer at.051 Hz, and has its first zero (other than 0 Hz) at ~.820+ Hz. The "A band" first approaches unity transfer at ~. 820 Hz, and has its first zero (other than at 0 Hz) at ~ 13.125 Hz. The crossover frequencies are fCB ~.026 Hz, f = ~.410 Hz. 47

Appendix B INDIVIDUAL POWER TRANSFER CHARACTERISTIC PLOTS 48

6, + X' r $ -/ — -... I --— *4/9s13+ee 1 -_*12 16 E+ JIl^^-^.A~~,-,IA~ *6.14496F+n, R "$PRE+n(j 001'1000IE. *7c1 7Ecinl f,,,-z *. 9z5s1^36! +-of + * RR49 8E+MF,~.; I ~~~~~~~~~~~~~~~~~~~~~9* 9 93'8 E+ rt ~ I * 9 8 6 ~.. +::, / I, l > 19 o I^^J~~~~ * ~'8l253E+(4q rt~Y; ~~I^-~ ]~iE ~9303s+,,?,^ - ^1 *9'1 7F+ iG1 0; L *R7r-,'^1E+,trz t ~ t g < I 3 (Ar~l y,, + Oe~~~~~~~~~to'94253 E+-.,'.*8 7 E927 +pr. cb ~' 1 7 3 E + r!;, * 95523E+rar~ tj ti *9,269- +:nn u, - L, I. 9R68P R +f r, *R$ 1r54PF +G1r.'? *' R$4*'.734 E+n2'"U'~~"79~ * IGR E+"!V~~~~~~~*1; +G9l5G); Cj' JL^/^ Z-^7l.'93r^S5~~~~~~63E+n'" *' 9 ~ 4 9?F': +1,') 21 4C *R 943F+983e I * I ~0094 0g+, I -~?. I'! | +~4+r4 JtI * 791734E+q,, ~1 f Ia..^.am+,,PI, L^-^l. r ^X ~S7 ^(,7E cH.,+ X l'~". iE+~] 1 1<"^^ f *"^^^'-.q1,,+ c~ ~7,o_~^ 10T0+ 0 ~o7I zQ 6 *".. +0 1 ~ l6'+,q /~~~~~~~)to~n

.4 a c cl^ ^: ^ ^~<-~.(5; c {^ ^ ^2 iQ_ ^ c^ ^ r^ ~- ^l ct (^^ ^t -~I ct S. G " - C 4- G m G (S. C~ a Ist G Is (IS C C & S C C C- C m G C C. 0 C I a a GI C G (S., C IS C. IS) CD (S CS a ED C.: S6 C. (' C G CS C r- nS C C, a; C a + + + + +.+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + U 13 iL l W W W W Le W & W W LO f rj xi ) &I ~W LO LL!21 fzj fIJ W ul Il iJF3 U Lr W fe W W L W W t W W W W W W w W L-) U j 6 W a d W U "21 L ( 3 L. tj Lu; W xi' W L Gj L Li %o v r- is r) &- o m r- q, c-m %D m 7 -- - - p c- c a, N6 C (; M, L n (s - - r- (s fl- - - n - 3~ CV) r- C" c, is,: - a (S q C) a a S C),: 6 C, C. + I V ON ts 6l C C,,) rGis (V) r t ) C C n q S- cO S CC, (S; 0 sCY C CG C Cm n ci Ln r'! a 6 t,- cyr: E c oj - t- qG j c- 6 oj E q Lr c (v r CO C' (V') ( d M No J) C M Lc> n or C -7 (V) r- a m n & C. G C UO (S. C (S CZ C, (S C c C C C G.' S C ) C ~ CD IS > ) C S t)P I G r ) M Is X c o %O a C, l r r- C (:C 0 C Or r CC CI I 6 7(Ct. Cr - -cc l~,, 0`1 ~c"~:aOc ChC r~ CC~C~ *t n 4C;1 + sin(ff 1~ 6f T) 2 -sin(?rl 6f T) +I 1+ 116 2 -2 16f cos (15-2k) V fT l 6sin(irf T) 1 6sin(irf T) 44o 8.0 Hz 16 Fig. 19. Individual power transfer characteristic, k =l, 14

^6 d ~I <SG a^ ti <r o C ln ts ln v co S c~ ~',, ""s c ~'' Nr -<( G " - s CS< rC-, f c- - C.,- -^, c^ r c^ ^I -. cr ~Ls C5 sc J- w j- r- n G iyfi' CK -- is Ca G? c0 D^Ec yG ^ -^^^^^^ - ^ - G isI - -- - is:L. (S C C: FS C G -^; G C a aa: C G C 6 a C h S G (:; Cs~ + + 4 ++ ++ +C * 44+4+ +++++++++++++++ +++ +44+4+ ++++++ +4+ +4+4 ~~t: I~~~r: tt~~~~ i] tt~ Lt~~~~~~:zl Ltl t! r~~~~~~~l W i] It: W i' ~~~~~~~~~tf W tl L i' tyEl.' W bL xi Lr 1) JmL Lx?? 6 ~I"" E c f< ~r: <??CT c ^ s ^ h 6 "r GI( t G ^'~ s c: L" os <s C^ - cn s- n 6 -' (r L' CL A W Le I L-t t- r+ - + +; + C' C C- C C- r. C5 - < *...^^^a -Z IS C L r C fSC' CC O* q PEC IS C; (: 1 C, C r r.r*S- c LriO O~ X C. r, C\ C- C C"~ C 6 —b ~ ~- c- Ci, + sin(rl 6f 7 2 sin(vl UT)7 1 sn(7T16U7j 2 - 2 (1 cos (15-2k) ffr 1 6sin(af T) 1 6sin(vfTr) 4Fig. 20. Individual power transfer characteristic, k=2, 13Hz Fig. 20. Individual power transfer characteristic, k 2, 13

F 6 6 K s - 6.S:-6 G- - -- ~ s 6: — e - -c - s -- -3 6 c, ~- " c 0'- - -- - - -, - - s - e; e - - - < - - -- E - - -. (- St. S C6 C C C C C a s 9 6 - C C 2 5., 6C t; C C S t C, C( C, C C Cs C, C; ^. C G 6.. C - C- E Z 4 C, C- C C _- C C C.' + + +, + + + + + + + + + + + + + + + + + + + + + + + 4+ + + ++ + + + + + + + + + + ++ + +4+ ++ +; - t ^' i @; i i; i 9 k S S ^ S LX E i iW E Ji; T L2 L f L t. Fg 21 Id cvda p r< -- e- - - - c.a r —-ei tk; 1-. -F *,'* -@ @-**e@ - *- *** —*v —.........~*.....**........ r, J) 6 V OC lO 115 C C1~ 6 C) C) C~ Ct C~ 6 F, CI 04 bC ~~ C~(C 6 6 C~ 6;3~ 6 ~' 6 6 6 2 os( 5 2) f Fig. 21.Iv6sin(a T) 1tr6sin(7r f T) ^ t *-' *' 8.0 Hz —- 16, H Fig. 21. Individual power transfer characteristic, k=3, 12

* C CCC~~~~~~~~~~~~~~~IC( 6'6 6 c 61~~~ Q - —, c cl - ~~ I ct c 6 G~~ O - c - ~~ c c cl c ~~-~ ~~ ~: s c ~ 6 ~~,c( cl,,h. - -C( - C. LC S Zs (S (I -M- it- C CC (S C PI: I *+++++++++++++++++++++.*++++4 +++++++++++ +++++++++ +++4++ W W W 4j W LsrlLJ t ~ WL W W W LLI L W Lt. Ll a a U.4 —P W Lx') Ltl L L: ) ~.j Lx1 GA W L! (.~ fjL~ tJ x2 No CV). a) S l C, j - S C.,C" C 0J. Lf J 0,C L ",C-7 C'47,C) n C:V ) (X 0, X isC-1 Y - U C ) C rL C. Lr C) V C 4- ". a0 CV C q C;na'4 J) S P ~ aP D~ a N C M N l C c C IC C "" (S. CV ~ a J) T \C' 7 (S r- \f) - C ct"'q S Tc I- e Cr l:^ 4) S IS M W S t- q C 0, N Z) (S C U -) T) -,C S \ -o N7 - C C - \C C un'7 ~ ~ Cm c r h 7' Ln C 0 - "C S - \C C %C J) J) C a \!6~, 0 1 CW:r ~C - CM S'q N I COJ CQ C 7 a\ G O a O C a C L - C (S - C C C\J Q Ck C C - ME a Z C O' f q C' S C.- C Z C V O q T 7! S! ^1? ^! ^?? ^???"?? K?? 6+???? ^?' ^^?? ^?* ^?? ^" ^ ^^ ^^ C, Y or 1t + F sin(vl 6f T1 2 2in 7 l 6f T cos (1 5 - 2k) f T [l6sin(iif r) I6sin(irfrf S 2 F 82 0 Hz k 11 Fig. 22. Individual power transfer characteristic, k 4, 11

S S S C CS S' a E C'S C I'S'S C S Z. C s rS. IS(S. C C C. a a (S; (S a (S C. Z G S S C C C (S C C + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +' + + + + + + + + + + + + a -7 Ii J tP CC (), S P- IS IS ISc' s 0\ MS C' c cO C, cv \N C; \.C S' O'.iC C'S CIf:.. C T _ _........... ~.~... ************a******************' _ - o.II sin(fl 6fJ 2 sin(vl 6f T) I 1 + | _16sin(^ r)J, - 2 cos (1 5 - 2k) 71f T 0 88.0 Hz --- 16 Fig. 23. Individual power transfer characteristic, k=5, 10

+ -G K -'- - -— &*~ - -C C S - -<^<- - C.C ~ -<-.-^-^<SG C <-C S C - -~- - - C.G (S -*- -~-'- (S.G-C -*- <c C - ^ - - -.C &-~~~~~~~~~~~~C. C C I' ~+~-~+4+++++++++ +++++++++++,>++++,++4 +^**+~+*4+.i' Wx Ex~ Ul Wj tej I) ExJ Lz, Fi-i U2 Wj WA lx? W~'~ %L. i W ~xJ uJ ~ Li-;^. Lz; 1jL:1~L Uix IxW Le 1 U (.11:Z: LLtJ^ I' LO Ixj *L~ 1x -L[xi.- td,X ~J - i l)UlI. LtJ fe,7- s xjW L: IxJ 1x Ez: EA ) W;'W -i LJ UL) Li W EL C,,~~~~~~~~~~~~~~~~~~~~~~~~~~aC 1+sin(vl16fr 2 - sin(7rl6f~z~( 1 6sin(vf -r C6Sin(11foscos 5-2k) Rf T I 1 ^ fsinfal~~~~~~~fT)'] 2 ~1 sin~rlf T) -.,\ 0 O Hz Fig. 24. Individual power transfer characteristic, k= 6, 9

I + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + W L, Lc: W C. [.~ Lt L [. L Lt. t.z L,.;- I. iJ zJ Lt. Lt J [. (M WI L.:.,''I [:,' Lz Li-.-'.: 0! LL''Ld ~ [L -; M y LL * G --... e'- G:... ), ~r o rX2 0 Lr) t c — +., C, 6f, )....2 s o(..6f.) co, (15-2k) irfT \...... Ll6sin(7rfT)J 16sinfl(1fT) 8.0 16, Fig. 25. Individual power transfer characteristic, k=7, 8

Appendix C TRIBAND GRAPHICAL RESULTS 57

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Appendix D TRIBAND CORRELATION RESULTS 82

The correlation coefficient is calculated over N points (N- 56, 126), which corresponds to approximately 28 and 63 minutes respectively. The coefficients given are between the noise band and the incoherent band (NI), the coherent band and the incoherent band (CI), and the noise band and the coherent band (NC). 83

CORRELATION COEFF. CALC. ENTER: # OF BLKS TO CORRELATE 4 # OF POINTS OUT 101 STARTING -BN 11 OF WORDS/GROUP (MODULUS)18 NI CI NC *768221 E+00 -.542124E+00 -.733997E:+00.926979E+00 -.775295E+00 -.506757E+~0.957398E+00.778901E-02 -.270941E+00 169689E+0. 187681E+00.365603E+00.536119E+00 -.182419E+00.7319874E+P0,.944009E+00 -.742966E+00 -.51C0669E+,P -340773E+00.81 8059E+00.5177g5E+0e -.257064E+00.604959E+00.601715E+00 -.434693E+00 -.316658E-02 - 832296E+(00.969706E+00 -.664729E+00 -.61 1603E+0.281939E+00.325287E-01 -. 940746E+00.738934E+00 -.747881E+00 -.435344~E+00.993000E+00 -.452549E+00 -.363563E+00.949059E+00o.780659E+00.800856E+00.999433E+00.1 07301E+00 *1 40699E+00.960022E+00. 743302E+00.676333E+00 ~555985E+00.768872E+00.793511E+00.917272E+00 - 187870E+00 -.536524E+00.996137E+00. 652237E+00.656486E+00.867264E+00 -.*984310E+00 -.771752E+00 -914644E+00.464299E+00.701939E+00.814554E+00 -.289185E-01 - 186831E+00.851 162E+00 -.520266E+00 -. 565044E+O3.999722E+00 -.555096E+00 -. 544291E+FJ.230898E+00.368665E+00 -. 553661E+0 0.669264E+00.473671E+00 -. 323476E+00 -.865385E+00 -.339377E+00.527417E+00..999689E+00.337793E+00.3 59532E+00 -.701170E+00,986490E+00 -.731123E+00 * 999825E+000 *- 441726E+0'0 -.5352 1 E+00 *614327E+00 - * 906397E-01.384483E-01 *892296E+00 -.452402E+00 -.527684E+00.661658E+00.70Q5135E+001. 947424E+00 * 973620E+00.846775E+00.808879E+00 988.96 I E+00 -.467819E+00 -558615E+00 *996962E+00 -. 143725E-01 -.658061E-01 *810422E-01.4&6479E+00 -.619173E+00 -.323337E+00o 31:'?93E+00.779649E+00.9976&2E+00.773150E+00.778983E4+00 -.449597t+00.278002E+00 -.879379E+00 -.871714E+00.338151E+00 -.278595E+00 997636[+00 -.46832E+00 -.51 9870E+00 -.341636E+00 -* 58330E+00 - * 1802Z42E+00. 999797?7E'+t00 - 7 35E+00 -.763856E+00..514344E4+10:.:1-$50E+00 * 547830E+00.,1 1 624L,00 +ee.a:478E+00 -.486910E+00.99&:6:6l;+'E -a::66770E+00 -. 955783E+00 * 979?95.+e0::i2l62E+00.17291 4E+00 84

.726162E+00.4 1429 IE+00 94994E+00 *999954E+00.623132E+0P.626142E+00 * 38904E+00 - ~.39644E+n -.985591E+n0. Q93480E+00..574350E+n0.663480F+00 * 99989E+00.79RI93E+00.79 8P22E+0'0.253791E+00.120176E+0P.B16098E+00.6539P9E-01.387f469E+0 -.342827E+00.966682E+00.9S88004E+00.980031E+00. 85460 1 E+00.~ 889089E+00. 864674E+00.97877RIE+00.840500E+00.889653E+00.656099E-02.508176E+00 -.569927E+00 999779E+00 -.516825E+00 -.50 1038E+0.978133E+00. 126307E+00 -.781789E-01.867979E+00 -.215186E+00 -.649876E+00.944P6 1E+00. 996964E+00.921924E+00.972978E+00.817879E+00.99589E+00 466999E+00 *.740385E+00~.404221E+00.996405E+00 -.316869E+00 -.258065E+00 *994249E+00.345256E+00.435147E+00.72420 E+00.812568E+00. 97379E+00 -.660804E+00 -.834162E+00.181967E+00 -. 17367E-01.822743E+00.548489E+00.999196E+00 -.599530E+00 - 573428E+00 99881 E+00 -.634921E+~0 -.668882E+00: 120921E+-0 -.791588E+0P -.100632E+00 - 999732E+00 -.924493E+00 -.918767E+00 - 186241E-01.252421E+00 -.212692E+00.784799E+00.973275E+0O.675830E+00.713447E+00.349012E+00.209448E+00 49496BE+00 -.230740E+00 -.435058E+00.999989E+00 -.481386E-01 - 506869E- 1.982829E+00.768324E+00.848301E+00 -997523E+00.988864E+00.976361 E+00 *99978 1E+00 - 894663E+00 -. 93824E+00.6681 6 1E-01.312382E+P0 ~ 444920E+00.996205E+00.*400714E+00.319960E+00.969996E+00 - 1S034E+00 -.416844E+00 955251E+00.479900E+00.203257E+00.235283E+00.807237E-01 -.92782E+00.867805E+00 -.372860E-02 -.302750E+00.999964E+00 -.695337E-01 -.70100E-01.985296E+00 *.25042E+00. 8 14015E+00.417991E+00.993556E+00.493243E+00.651386E+00. -.656501E+00 -.103448E+00[ ~ 940862E+00 -.740468E+00 -.724225E+00.997688E+00 -.29 t692E+f00 -.330573E+00.867174E+00.811273E+001 ~ -.253211E+00 979536E+00 -.543909E+00 -.694728E+00 *974991E+00.924934E+00.938515E+00 999840E+00 * 184394E+00. 1940S7E+O0 ~*991547E+00.132269E+00.264507E-02 * 998893E+00 -. 91 0943E+00 -.916101E+00 -.221869E+00 -.563108E+0e0.358225E+00 85

CORRELATION COEFF. CALC. N=126, T63 min ENTER: # OF BLKS TO CORRELATE 9 # OF POINTS OUT 45 STARTING BN 1 # OF WORDS/GROUP (MODULUS) 18 NI CI NC.852521E+00 -.451818E+00 -.413810E+00.965293E+00.452103E+00.417518E+00.271267E+00.486654E+00.894976E-01 -.219954E+00.664379E-02 -.262184E+00.969504E+00 -.421431E+00 -.449434E+00 *992848E+00 -.373550E+00 - 345961E+00 *725915E+00 -.391727E+00 -.448813E-01.731281E+00.803340E+00.882236E+00 *950645E+00 -.462754E-01.461742E-01.719960E+00 -. 160394E+00 - 358782E+i00.999403E+00 -.365771E+00 -.375217E+00 *438516E+00 -.440403E-01.322034E+00 *781975E+00.481732E+00.405829E+00.247757E+00 -.120055E+00.380538E+00.5 11026E+00.248759E+00.173346E+00.991362E+00 1 96140E+00. 186905E+00. i 163457E+00.353114E+00.556800E+00.962848E+00 -.178149E+00 -.166681E+00.744339E+00 -.305367E+00 195839E-01.999921 E+00 -. 176095E+00 -.172884E+00.997624E+00.275327E+00.283125E+00 *931072E+00 -.297992E-01 -.246240E+00.909777E+00 -.739983E-01.771458E-01.999825E+00.668380E+00.678429E+00 *210524E+00 -.824114E-01 -.348032E+00.978387E+00 184003E+00.288743E+00.794899E+00 -.420493E+00 -.734091E+00 *928913E+00.213553E+00.13421 IE+00 *794454E+00.361621E+00.547159E-01 *986533E+00 -.175782E+00 -.492371E-01 -.759288E-01.444894E+00.309548E+00 *998951E+00.273988E+00.276698E+00 *461461E-01 -.291178E+00 -.243310E+00 *380683E+00.451562E+00 -. 191874E+00 *999869E+00 -.246232E+00 -.250361E+00 *873230E+00 * 176823E+00.289996E+00.99?037E+00 -.800729E+00 -.805181E+00.917364E+00.549639E+00.416587E+00 *240118E-01.672639E+00 -.291275E+00 *999798E+00.21 8474E+00.212479E+00.216353E+00.936935E-01 * 138660E+00.882526E+00 -.434039E+00 -.327080E+00 * 893548E+00 -.466099E+00 -.471308E+00.979042E+00 * 196885E+00 * 124680E+00.986949E+00 -.491378E+00 -.3888 17E+00 86

REFERENCES 1. Morton Kronengold and William J. Toulis, "Directional 420-Hz Sound Source, " IEEE Transactions on Geoscience Electronics, Vol. GE-6, No. 4, November, 1968, pp. 204-24. 2. R. Unger and R. Veenkant, Underwater Sound Propagation in the Straits of Florida: The Mimi Experiment of 3 and 4 February 1965, Technical Report No. 183 (3674-12-T), Cooley Electronics Laboratory, The University of Michigan, Ann Arbor, Michigan, May 1967. 87

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Se,'uritv Classification l4. LINK A LlNK B LINK C KEY WORDS, Signal Processing KEY W ORDS |ROLE WT ROLE I WT ROLE WT Signal Processing Acoustic Propagation Digital Filtering i I i:1,, tt s I' DD,FO. RM,1473 (BACK) S/N 0101-807-6821 Security Classification A — 31409

1 Security Classification DOCUMENT CONTROL DATA - R & D (Security classification of title, body of abstract and indexing annotation must be entered when the overall report is classified) I ORIGINATING ACTIVITY (Corporate author) 2a. REPORT SECURITY CLASSIFICATION Cooley Electronics Laboratory Unclassified The University of Michigan 2b. GROUP Ann Arbor, Michigan 48105 3. REPORT TITLE Triband: The Three Band Filter for the Continuing MIMI Experiment 4. DESCRIPTIVE NOTES (Type of report and.inclusive dates) Technical Report No. 201 - 03674-24-T 5. AU THOR(S) (First name, middle initial, last name) Hatter, Norman 6. REPORT DATE 7a. TOTAL NO. OF PAGES 7b. NO. OF REFS February 1970 102 2 8a. CONTRACT OR GRANT NO. 9a. ORIGINATOR'S REPORT NUMBER(S) Nonr-1224(36) b. PROJECT NO. 03674-24-T | NR187-200 C. 9b. OTHER REPORT NO(S) (Any other numbers that may be assigned this report) d. TR201 10. DISTRIBUTION STATEMENT Reproduction in whole or in part is permitted for any purpose of the U.S. Government. I 1. SUPPLEMENTARY NOTES 12. SPONSORING MILITARY ACTIVITY Office of Naval Research I0j~~~~~ | ~Department of the Navy J# ~___~~____________Washington, D. C. 20360 13. ABSTRACT An experiment was conducted as part of the continuing study of sound propagation in the Straits of Florida. A 420-Hz continuous wave (CW) signal was transmitted, received at the 7-mile hydrophone, and processed by the Linc-8 on-line digital processor. The processing yielded the magnitude and phase of the reception in a 1/16-Hz band, the magnitude of the reception in a 1-Hz band but excluding the 1/16-Hz band, and the magnitude of the reception in a 16-Hz band that excluded the 1-Hz band. All bands were centered at 420 Hz. The purposes of the experiment were to verify the possibility of such a three-band analysis and to obtain "typical" relative power ratios to aid in the design of analog triband phase coherent demodulation. DD "FORM"1473 (PAGE 1 ) S/N 01 01 -807-6811 Security Classification A-31408