On the statistics of estimated reflection and cepstrum coefficients of an autoregressive process

Abstract A common assumption in most theoretical and applied works is the Gaussian assumption. Many signal processing tools have been developed using this Gaussian hypothesis. But in recent years, non-Gaussian processes have been considered with increasing interest. New techniques, such as those based on higher order statistics, have been studied for these processes. Thus, the Gaussian or non-Gaussian nature of signals, parameters or estimators has to be indicated. The aim of this paper is to study the statistical properties of estimated reflection and cepstrum coefficients. First, a recursive way of computing their probability density function (p.d.f.) from that of estimated AR parameters is proposed. Then, these probability density functions are compared to the Gaussian law. The last part of the paper is developed to the study of the convexity of the p.d.f. Through examples, they are shown to be possibly non-convex, yielding a case in which the centroid distance classifier may result in a failure.