The spectral analysis of impulse processes

An expression for the spectral density of the impulse process s(t) = {if236-1} is derived under the assumption that \αn\}} is a stationary process, and that \tn\}} is a stationary point process independent of \αn\}}. The spectral density appears as an infinite series in terms of the correlation of \αn\}} and the interval statistics of \tn\}}. 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 \αn\}} and \tn\}}.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