The spectral analysis of impulse processes

Abstract

An expression for the spectral density of the impulse process s(t) = {if236-1} is derived under the assumption that [alpha]n}} is a stationary process, and that n}} is a stationary point process independent of [alpha]n}}. The spectral density appears as an infinite series in terms of the correlation of [alpha]n}} and the interval statistics of n}}. The same result was obtained by Leneman by a different argument under considerably more restrictive conditions of validity.Various models of impulse processes are discussed relative to random sampling of random processes. Random and systematic loss of samples, separate read-in and read-out jitters, and correlated random scaling errors can all be represented by appropriate assumptions on [alpha]n}} and n}}.Finally, closed form expressions are calculated for the spectral density of s(t) and the sampled process under combinations of the sampling errors mentioned in the preceding paragraph.