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An Introduction to Statistical Signal Processing

By Gray, Robert M.

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Book Id: WPLBN0000661978
Format Type: PDF eBook
File Size: 1.8 MB
Reproduction Date: 2005
Full Text

Title: An Introduction to Statistical Signal Processing  
Author: Gray, Robert M.
Volume:
Language: English
Subject: Science., Mathematics, Logic
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Gray, R. M. (n.d.). An Introduction to Statistical Signal Processing. Retrieved from http://worldebookfair.org/


Description
Mathematics document containing theorems and formulas.

Excerpt
Excerpt: The origins of this book lie in our earlier book Random Processes: A Mathematical Approach for Engineers, Prentice Hall, 1986. This book began as a second edition to the earlier book and the basic goal remains unchanged ? to introduce the fundamental ideas and mechanics of random processes to engineers in a way that accurately reflects the underlying mathematics, but does not require an extensive mathematical background and does not belabor detailed general proofs when simple cases suffice to get the basic ideas across. In the thirteen years since the original book was published, however, numerous improvements in the presentation of the material have been suggested by colleagues, students, teaching assistants, and by our own teaching experience. The emphasis of the class shifted increasingly towards examples and a viewpoint that better reflected the course title: An Introduction: to Statistical Signal Processing. Much of the basic content of this course and of the fundamentals of random processes can be viewed as the analysis of statistical signal processing systems: typically one is given a probabilistic description for one random object, which can be considered as an input signal. An operation or mapping or filtering is applied to the input signal (signal processing) to produce a new random object, the output signal. Fundamental issues include the nature of the basic probabilistic description and the derivation of the probabilistic description of the output signal given that of the input signal and a description of the particular operation performed. A perusal of the literature in statistical signal processing, communications, control, image and video processing, speech and audio processing, medical signal processing, geophysical signal processing, and classical statistical areas of time series analysis, classification and regression, and pattern recognition show a wide variety of probabilistic models for input processes and for operations on those processes, where the operations might be deterministic or random, natural or artificial, linear or nonlinear, digital or analog, or beneficial or harmful. An introductory course focuses on the fundamentals underlying the analysis of such systems: the theories of probability, random processes, systems, and signal processing.

Table of Contents
Contents Preface xi Glossary xv 1 Introduction 1 2 Probability 11 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Spinning Pointers and Flipping Coins . . . . . . . . . . . . 15 2.3 Probability Spaces . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.1 Sample Spaces . . . . . . . . . . . . . . . . . . . . . 28 2.3.2 Event Spaces . . . . . . . . . . . . . . . . . . . . . . 31 2.3.3 Probability Measures . . . . . . . . . . . . . . . . . . 42 2.4 Discrete Probability Spaces . . . . . . . . . . . . . . . . . . 45 2.5 Continuous Probability Spaces . . . . . . . . . . . . . . . . 56 2.6 Independence . . . . . . . . . . . . . . . . . . . . . . . . . . 70 2.7 Elementary Conditional Probability . . . . . . . . . . . . . 71 2.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3 Random Objects 85 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 3.1.1 Random Variables . . . . . . . . . . . . . . . . . . . 85 3.1.2 Random Vectors . . . . . . . . . . . . . . . . . . . . 89 3.1.3 Random Processes . . . . . . . . . . . . . . . . . . . 93 3.2 Random Variables . . . . . . . . . . . . . . . . . . . . . . . 95 3.3 Distributions of Random Variables . . . . . . . . . . . . . . 104 3.3.1 Distributions . . . . . . . . . . . . . . . . . . . . . . 104 3.3.2 Mixture Distributions . . . . . . . . . . . . . . . . . 108 3.3.3 Derived Distributions . . . . . . . . . . . . . . . . . 111 3.4 Random Vectors and Random Processes . . . . . . . . . . . 115 3.5 Distributions of Random Vectors . . . . . . . . . . . . . . . 117

 

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