A First Course in Statistics for Signal Analysis

Front Cover
Springer Science & Business Media, May 26, 2007 - Technology & Engineering - 222 pages
0 Reviews
This essentially self-contained, deliberately compact, and user-friendly textbook is designed for a first, one-semester course in statistical signal analysis for a broad audience of students in engineering and the physical sciences. The emphasis throughout is on fundamental concepts and relationships in the statistical theory of stationary random signals, explained in a concise, yet fairly rigorous presentation. Topics and Features: Fourier series and transforms are developed from scratch, emphasizing the time-domain vs. frequency-domain duality. Basic concepts of probability theory, laws of large numbers, the stability of fluctuations law, and statistical parametric inference procedures are presented. Introduction of the fundamental concept of a stationary random signal and its autocorrelation structure. Many diverse examples as well as end-of-chapter problems and exercises. Developed by the author over the course of several years of classroom use, A First Course in Statistics for Signal Analysis may be used by junior/senior undergraduates or graduate students in electrical, systems, computer, and biomedical engineering, as well as the physical sciences. The work is also an excellent resource of educational and training material for scientists and engineers working in research laboratories.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Description of Signals
1
12 Time domain and frequency domain descriptions
8
13 Characteristics of signals
12
14 Problems and exercises
13
Spectral Representation of Deterministic Signals Fourier Series and Transforms
16
22 Approximation of periodic signals by finite Fourier sums
26
23 Aperiodic signals and Fourier transforms
31
24 Basic properties of the Fourier transform
35
54 Problems and exercises
124
Transmission of Stationary Signals through Linear Systems
127
61 The time domain analysis
128
62 Frequency domain analysis and system bandwidth
136
63 Digital signal discretetime sampling
140
64 Problems and exercises
144
Optimization of SignaltoNoise Ratio in Linear Systems
147
72 Filter structure matched to signal
151

25 Fourier transforms of some nonintegrable signals Dirac delta impulse
37
26 Discrete and fast Fourier transforms
42
27 Problems and exercises
44
Random Quantities and Random Vectors
47
31 Discrete continuous and singular random quantities
48
32 Expectations and moments of random quantities
62
33 Random vectors conditional probabilities statistical independence and correlations
67
34 The leastsquares fit regression line
77
35 The law of large numbers and the stability of fluctuations law
80
36 Estimators of parameters and their accuracy confidence intervals
82
37 Problems exercises and tables
86
Stationary Signals
93
42 Estimating the mean and the autocorrelation function ergodic signals
105
43 Problems and exercises
109
Power Spectra of Stationary Signals
113
52 Power spectrum and autocorrelation function
114
53 Power spectra of interpolated digital signals
121
73 The Wiener filter
154
74 Problems and exercises
156
Gaussian Signals Correlation Matrices and Sample Path Properties
158
81 Linear transformations of random vectors
160
82 Gaussian random vectors
162
83 Gaussian stationary signals
165
84 Sample path properties of general and Gaussian stationary signals
167
85 Problems and exercises
173
Discrete Signals and Their Computer Simulations
175
92 Cumulative power spectrum of discretetime stationary signal
176
93 Stochastic integration with respect to signals with uncorrelated increments
179
94 Spectral representation of stationary signals
184
95 Computer algorithms
188
96 Problems and exercises
196
Bibliographical Comments
197
Index
201
Copyright

Other editions - View all

Common terms and phrases

Bibliographic information