文档介绍：i
An Introduction to
Statistical Signal Processing
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January 4, 2011
ii
An Introduction to
Statistical Signal Processing
Robert M. Gray
and
Lee D. Davisson
Information Systems Laboratory
Department of Electrical Engineering
Stanford University
and
Department of Electrical Engineering puter Science
University of Maryland
c 2004 by Cambridge University Press. Copies of the pdf file may be
downloaded for individual use, but multiple copies cannot be made or printed
without permission.
iii
to our Families
Contents
Preface page ix
Acknowledgements xii
Glossary xiii
1 Introduction 1
2 Probability 10
Introduction 10
Spinning pointers and flipping coins 14
Probability spaces 22
Discrete probability spaces 44
Continuous probability spaces 54
Independence 68
Elementary conditional probability 70
Problems 73
3 Random variables, vectors, and processes 82
Introduction 82
Random variables 93
Distributions of random variables 102
Random vectors and random processes 112
Distributions of random vectors 115
Independent random variables 124
Conditional distributions 127
Statistical detection and classification 132
Additive noise 135
Binary detection in Gaussian noise 142
Statistical estimation 144
Characteristic functions 145
Gaussian random vectors 151
Simple random processes 152
v
vi Contents
Directly given random processes 156
Discrete time Markov processes 158
⋆Nonelementary conditional probability 167
Problems 168
4 Expectation and averages 182
Averages 182
Expectation 185
Functions of random variables 188
Functions of several random variables 195
Properties of expectation 195
Examples 197
Conditional expectation 206
⋆Jointly Gaussian vectors 209