Stochastic Signals and Estimation

Abstract

In this chapter, the authors review the basic concepts and tools which are required to deal with stochastic signals such as speech signals. Among these are random variables and stochastic processes as well as power spectra and fundamentals of estimation theory. Modern theory of probability defines the probability P(A i ) of an event A i on the basis of set-theoretic concepts and axioms, not on the basis of observed random phenomena. Conditional probabilities capture the notion of a priori information. The authors discuss some of the frequently used probability density functions and their moments. For the treatment of multivariate statistics, it is convenient to introduce vector notation. A stochastic process is called strict sense stationary if all its statistical properties (such as moments) are invariant with respect to a variation of k.

Authors 2

1. Peter Vary Aachen Institute of Communication Systems

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Institute of Communication Systems, Aachen, Germany

2. Rainer Martin

   Ruhr University Bochum

   Affiliation as printed

   Ruhr-Universität Bochum, Institute of Communication Acoustics, Bochum, Germany