Signal processing arises in the design of such diverse systems as communications, sonar, radar, electrooptical, navigation, electronic warfare and medical imaging systems. It is also used in many physical sciences, such as geophysics, acoustics, and meteorology, among many others. The common theme is to extract and estimate the desired signals, which are mixed with a variety of noise sources and disturbances. Signal processing involves system analysis, random processes, statistical inferences, and software and hardware implementation. The purpose of this book is to provide an elementary, informal introduction, as well as a comprehensive account of principles of random signal processing, with emphasis on the computational aspects. This book covers linear system analysis, probability theory, random signals, spectral analysis, estimation, filtering, and detection theory. It can be used as a text for a course in signal processing by under graduates and beginning graduate students in engineering and science and also by engineers and scientists engaged in signal analysis, filtering, and detection. Part of the book has been used by the author while teaching at the State University of New York at Buffalo and California State University at Long Beach. An attempt has been made to make the book self-contained and straight forward, with the hope that readers with varied backgrounds can appreciate and apply principles of signal processing. Chapter 1 provides a brief review of linear analysis of deterministic signals.