The Spectral Analysis of Impulse Processes

An expression for the spectral density of the impulse process s(t) = ~ :~ a~(t t,) is derived under the assumption that {an} is a s tat ionary process, and that {t~} is a stat ionary point process independent of {a~}. The spectral density appears as an infinite series in terms of the correlation of {a~} and the interval statistics of Its}. The same result was obtained b y Leneman by a different argument under considerably more restr ict ive 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 j i t ters, and correlated random scaling errors can all be represented by appropriate assumptions on {a~} and {t~}. 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.