TABLE OF CONTENTS Many situations occur that involve nondeterministic or random phenomena. Some common ones are the effects of wind gusts on the position of a television antenna, air turbulence on the bending on an airplane's wing, and magnitudes of systolic blood pressure. Similarly there are many signal and time series measurements with random characteristics. Their behavior is not predictable with certainty because either it is too complex to model, or knowledge is incomplete, or, as with some noise processes, it is essentially indeterminate. To analyze and understand these phenomena, a probabilistic approach must be used. The concepts and theory of probability and estimation provide a fundamental mathematical framework for the techniques of analyzing random signals.
It is assumed that the reader has had an introduction to probability and statistics. Hence this chapter will provide a brief summary of the relevant concepts of probability and random variables before introducing some concepts of estimation which are essential for signal analysis. If one desires a comprehensive treatment of probability and random variables from an engineering and scientific viewpoint, the books by Ochi (1990), Papoulis and Piliai (2002), and Stark and Woods (2002) are excellent; less comprehensive but also good sources are the books by Childers (1997), O'Flynn (1982), and Peebles (2001). If one desires a review, any introductory textbook is suitable. If one is interested in a comprehensive treatment of probability and statistics from an engineering and scientific viewpoint, refer to the books written by Milton and Arnold (2003) and Vardeman (1994).
