文档介绍：An Introduction to
Statistical Signal Processing
f −1(F )
f
F
Pr(f ∈ F )=P ({ω: ω∈ F })=P (f −1(F ))
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May 5, 2000
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
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c 1999 by the authors.
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to our Families
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Contents
Preface xi
Glossary xv
1 Introduction 1
2 Probability 11
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Spinning Pointers and Flipping Coins . . . . . . . . . . . . 15
Probability Spaces . . . . . . . . . . . . . . . . . . . . . . . 23
Sample Spaces . . . . . . . . . . . . . . . . . . . . . 28
Event Spaces . . . . . . . . . . . . . . . . . . . . . . 31
Probability Measures . . . . . . . . . . . . . . . . . . 42
Discrete Probability Spaces . . . . . . . . . . . . . . . . . . 45
Continuous Probability Spaces . . . . . . . . . . . . . . . . 56
Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Elementary Conditional Probability . . . . . . . . . . . . . 71
Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3 Random Objects 85
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Random Variables . . . . . . . . . . . . . . . . . . . 85
Random Vectors . . . . . . . . . . . . . . . . . . . . 89
Random Processes . . . . . . . . . . . . . . . . . . . 93
Random Variables . . . . . . . . . . . . . . . . . . . . . . . 95
Distributions of Random Variables . . . . . . . . . . . . . . 104
Distributions . . . . . . . . . . . . . . . . . . . . . . 104
Mixture Distributions . . . . . . . . . . . . . . . . . 108
Derived Distributions . . . . . . . . . . . . . . . . . 111
Random Vectors and Random Processes .