Distortion and estimation of the autocorrelation function and spectrum of a randomly sampled signal

Abstract

This thesis provides two additions to the theory of random sampling. The first is a new theory for predicting the autocorrelation function (ACF) and spectrum of thesampling process. In this theory the random sampling process is described by its time-varying mean sampling rate and the complete set of inter-sample probability density functions. These results are then used to determine the autocorrelation function and spectrum of a signal after sampling. The theory predicts the ACF for both the stationary and nonstationary cases, and does not use any of the "small deviation from equispaced sampling" assumptions required by many random sampling theories. Thus, from the model developed here, several new results have been obtained for important sampling processes previously untreated in the literature. Notable among these is an analysis of Poisson sampling with dead time. It is expected that this theory will find application in the error analysis of equispaced sample systems, design of optimized random sampling schemes for specific applications, and generalization of the theory of "shot noise".