An Introduction to Statistical Signal Processing

by Robert M. Gray , Lee D. Davisson

• ISBN13: 9780521838603
• ISBN10: 0521838606
• Format: Hardcover
• Copyright: 2005-01-24
• Publisher: Cambridge University Press

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