An Introduction to Statistical Signal Processing,9780521838603

An Introduction to Statistical Signal Processing

by
ISBN13: 9780521838603
ISBN10: 0521838606
Format: Hardcover
Pub. Date: 2005-01-24
Publisher(s): Cambridge University Press
List Price: $156.00

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Summary

This book describes the essential tools and techniques of statistical signal processing. At every stage theoretical ideas are linked to specific applications in communications and signal processing using a range of carefully chosen examples. The book begins with a development of basic probability, random objects, expectation, and second order moment theory followed by a wide variety of examples of the most popular random process models and their basic uses and properties. Specific applications to the analysis of random signals and systems for communicating, estimating, detecting, modulating, and other processing of signals are interspersed throughout the book. Hundreds of homework problems are included and the book is ideal for graduate students of electrical engineering and applied mathematics. It is also a useful reference for researchers in signal processing and communications.

Table of Contents

Preface ix
Acknowledgements xii
Glossary xiii
1 Introduction 1(9)
2 Probability 10(72)
2.1 Introduction
10(4)
2.2 Spinning pointers and flipping coins
14(8)
2.3 Probability spaces
22(22)
2.4 Discrete probability spaces
44(10)
2.5 Continuous probability spaces
54(14)
2.6 Independence
68(2)
2.7 Elementary conditional probability
70(3)
2.8 Problems
73(9)
3 Random variables, vectors, and processes 82(100)
3.1 Introduction
82(11)
3.2 Random variables
93(9)
3.3 Distributions of random variables
102(10)
3.4 Random vectors and random processes
112(3)
3.5 Distributions of random vectors
115(9)
3.6 Independent random variables
124(3)
3.7 Conditional distributions
127(5)
3.8 Statistical detection and classification
132(3)
3.9 Additive noise
135(7)
3.10 Binary detection in Gaussian noise
142(2)
3.11 Statistical estimation
144(1)
3.12 Characteristic functions
145(6)
3.13 Gaussian random vectors
151(1)
3.14 Simple random processes
152(4)
3.15 Directly given random processes
156(2)
3.16 Discrete time Markov processes
158(9)
3.17 *Nonelementary conditional probability
167(1)
3.18 Problems
168(14)
4 Expectation and averages 182(93)
4.1 Averages
182(3)
4.2 Expectation
185(3)
4.3 Functions of random variables
188(7)
4.4 Functions of several random variables
195(1)
4.5 Properties of expectation
195(2)
4.6 Examples
197(9)
4.7 Conditional expectation
206(3)
4.8 *Jointly Gaussian vectors
209(2)
4.9 Expectation as estimation
211(7)
4.10 *Implications for linear estimation
218(3)
4.11 Correlation and linear estimation
221(7)
4.12 Correlation and covariance functions
228(3)
4.13 *The central limit theorem
231(3)
4.14 Sample averages
234(2)
4.15 Convergence of random variables
236(7)
4.16 Weak law of large numbers
243(2)
4.17 *Strong law of large numbers
245(4)
4.18 Stationarity
249(6)
4.19 Asymptotically uncorrelated processes
255(3)
4.20 Problems
258(17)
5 Second-order theory 275(88)
5.1 Linear filtering of random processes
276(2)
5.2 Linear systems I/O relations
278(6)
5.3 Power spectral densities
284(2)
5.4 Linearly filtered uncorrelated processes
286(6)
5.5 Linear modulation
292(4)
5.6 White noise
296(3)
5.7 *Time averages
299(4)
5.8 *Mean square calculus
303(28)
5.9 *Linear estimation and filtering
331(18)
5.10 Problems
349(14)
6 A menagerie of processes 363(48)
6.1 Discrete time linear models
364(5)
6.2 Sums of iid random variables
369(1)
6.3 Independent stationary increment processes
370(3)
6.4 *Second-order moments of isi processes
373(3)
6.5 Specification of continuous time isi processes
376(2)
6.6 Moving-average and autoregressive processes
378(2)
6.7 The discrete time Gauss-Markov process
380(1)
6.8 Gaussian random processes
381(1)
6.9 The Poisson counting process
382(3)
6.10 Compound processes
385(1)
6.11 Composite random processes
386(1)
6.12 *Exponential modulation
387(5)
6.13 *Thermal noise
392(3)
6.14 Ergodicity
395(3)
6.15 Random fields
398(2)
6.16 Problems
400(11)
Appendix A Preliminaries 411(25)
A.1 Set theory
411(7)
A.2 Examples of proofs
418(4)
A.3 Mappings and functions
422(1)
A.4 Linear algebra
423(4)
A.5 Linear system fundamentals
427(4)
A.6 Problems
431(5)
Appendix B Sums and integrals 436(10)
B.1 Summation
436(3)
B.2 *Double sums
439(2)
B.3 Integration
441(2)
B.4 *The Lebesgue integral
443(3)
Appendix C Common univariate distributions 446(2)
Appendix D Supplementary reading 448(5)
References 453(4)
Index 457

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