Signal Processing: Signals, Filtering, and Detection

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.

Table of Contents:
1. Signals, Spectra, and Samples.- 1.0. Introduction.- 1.1. Signals.- 1.2. Fourier Series.- 1.3. Fourier, Laplace, and Hubert Transforms.- 1.4. Linear Systems and Filters.- 1.5. Sampling.- 1.6. Digital Signals and Discrete Transforms.- 1.7. Matrix and State Variable Methods.- 1.8. Bibliographical Notes.- Exercises.- Appendix 1.A. The Fast Fourier Transforms.- Appendix 1.B. Zeros and Poles.- Appendix 1.C. Proofs of Fourier, Laplace, and z Transforms.- Appendix 1.D. Digital Filter Fundamentals.- 2. Random Samples.- 2.0. Introduction.- 2.1. Probability Space.- 2.2. Probability Assignment.- 2.3. Random Variable.- 2.4. Moments and Characteristic Function.- 2.5. Functions of Random Variables.- 2.6. Multidimensional Random Variable.- 2.7. Conditional Probability: Distribution and Density.- 2.8. Distribution Associated with Gaussian Variables.- 2.9. Bibliographical Notes.- Exercises.- Appendix 2.A. Cauchy-Schwarz Inequality.- 3. Random Signals, Estimation, and Filtering.- 3.0. Introduction.- 3.1. Definition and Description.- 3.2. Correlation and Covariance Functions.- 3.3. Gaussian and Markov Processes.- 3.4. Stationary Random Signals.- 3.5. Spectral Analysis and Sampling.- 3.6. Narrow Band Noise Process.- 3.7. Estimation of Parameters.- 3.8. Estimation Methods.- 3.9. Recursive Estimation.- 3.10. Optimum Linear Filters.- 3.11. Bibliographical Notes.- Exercises.- Appendix 3.A. Spectral Estimation.- Appendix 3.B. Kaiman Filtering.- 4. Detection of Signals.- 4.0. Introduction.- 4.1. Hypothesis Testing.- 4.2. Signals with Known Parameters.- 4.3. Signals with Random Parameters.- 4.4. Signals in Colored Noise.- 4.5. Multiple Signals.- 4.6. Sequential Detection.- 4.7. Nonparametric Methods.- 4.8. Bibliographical Notes.- Exercises.- Appendix 4.A. Two Double-Integral Identities.- Appendix 4.B. Link Calculation for Satellite Communication and Rain Attenuation.