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E-raamat: First Course in Statistics for Signal Analysis

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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 transformsfundamentally important in random signal analysis and processingare developed from scratch, emphasizing the time-domain vs. frequency-domain duality;





·         Basic concepts of probability theory, laws of large numbers, the central limit theorem, and statistical parametric inference procedures are presented so that no prior knowledge of probability and statistics is required; the only prerequisite is a basic twothree semester calculus sequence;





·         Computer simulation algorithms of stationary random signals with a given power spectrum density;





·         Complementary bibliography for readers who wish to pursue the study of random signals in greater depth;





·         Many diverse examples and end-of-chapter problems and exercises.





Developed by the author over the course of many years of classroom use, A First Course in Statistics for Signal Analysis, Second Edition 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. This third edition contains two additional chapters that present wavelets and the uncertainty principle, and the forecasting problems for stationary time series. These two topics are essential for students to attain a deeper understanding of statistical analysis of random signals.

Reviews from previous editions:





A First Course in Statistics for Signal Analysis is a small, dense, and inexpensive book that covers exactly what the title says: statistics for signal analysis. The book has much to recommend it. The author clearly understands the topics presented. The topics are covered in a rigorous manner, but not so rigorous as to be ostentatious.  JASA (Review of the First Edition)





This is a nicely written self-contained book and it is a good candidate for adoption as a textbook for upper-level undergraduate and even for a graduate course for engineering and physical sciences students. I have no hesitation in recommending it as a textbook for the targeted course and audience.  Technometrics, Vol. 53 (4), November, 2011 (Review of the Second Edition)
Part I
1 Description of Signals
3(22)
1.1 Types of Random Signals
3(8)
1.2 Characteristics of Signals
11(1)
1.3 Time Domain and Frequency Domain Descriptions of Periodic Signals
12(7)
1.4 Building a Better Mousetrap: Complex Exponentials
19(3)
1.5 Problems and Exercises
22(3)
2 Spectral Representation of Deterministic Signals: Fourier Series and Transforms
25(32)
2.1 Complex Fourier Series for Periodic Signals
25(10)
2.2 Approximation of Periodic Signals by Finite Fourier Sums
35(6)
2.3 Aperiodic Signals and Fourier Transforms
41(3)
2.4 Basic Properties of Fourier Transform
44(3)
2.5 Fourier Transforms of Some Non-integrable Signals: Dirac's Delta-Impulse
47(4)
2.6 Discrete and Fast Fourier Transforms
51(2)
2.7 Problems and Exercises
53(4)
3 Uncertainty Principle and Wavelet Transforms
57(34)
3.1 Time-Frequency Localization and the Uncertainty Principle
57(3)
3.2 Windowed Fourier Transform
60(5)
3.3 Continuous Wavelet Transforms
65(13)
3.4 Haar Wavelets and Multiresolution Analysis
78(6)
3.5 Continuous Daubechies' Wavelets
84(5)
3.6 Exercises
89(2)
4 Random Quantities and Random Vectors
91(60)
4.1 Discrete, Continuous, and Singular Random Quantities
91(22)
4.2 Expectations and Moments of Random Quantities
113(4)
4.3 Random Vectors, Conditional Probabilities, Statistical Independence, and Correlations
117(12)
4.4 The Least Squares Fit, Linear Regression
129(4)
4.5 The Law of Large Numbers and the Stability of Fluctuations Law
133(3)
4.6 Estimators of Parameters and Their Accuracy: Confidence Intervals
136(8)
4.7 Problems and Exercises
144(7)
Part II
5 Stationary Signals
151(24)
5.1 Stationarity and Autocovariance Functions
151(15)
5.2 Estimating the Mean and the Autocovariance Function, Ergodic Signals
166(4)
5.3 Problems and Exercises
170(5)
6 Power Spectra of Stationary Signals
175(18)
6.1 Mean Power of a Stationary Signal
175(2)
6.2 Power Spectrum and Autocovariance Function
177(7)
6.3 Power Spectra of Interpolated Digital Signals
184(5)
6.4 Problems and Exercises
189(4)
7 Transmission of Stationary Signals Through Linear Systems
193(24)
7.1 Time Domain Analysis
193(9)
7.2 Frequency Domain Analysis and System's Bandwidth
202(4)
7.3 Digital Signal, Discrete Time Sampling
206(6)
7.4 Problems and Exercises
212(5)
Part III
8 Optimization of Signal-to-Noise Ratio in Linear Systems
217(12)
8.1 Parametric Optimization for a Fixed Filter Structure
217(4)
8.2 Filter Structure Matched to Input Signal
221(3)
8.3 The Wiener Filter
224(3)
8.4 Problems and Exercises
227(2)
9 Gaussian Signals, Covariance Matrices, and Sample Path Properties
229(18)
9.1 Linear Transformations of Random Vectors
229(3)
9.2 Gaussian Random Vectors
232(5)
9.3 Gaussian Stationary Signals
237(2)
9.4 Sample Path Properties of General and Gaussian Stationary Signals
239(6)
9.5 Problems and Exercises
245(2)
10 Spectral Representation of Discrete-Time Stationary Signals and Their Computer Simulations
247(32)
10.1 Spectral Representation
247(2)
10.2 Autocovariance as a Positive-Definite Sequence
249(2)
10.3 Cumulative Power Spectrum of Discrete-Time Stationary Signal
251(3)
10.4 Stochastic Integration with Respect to Signals with Uncorrelated Increments
254(5)
10.5 Spectral Representation of Stationary Signals
259(4)
10.6 Computer Algorithms: Complex-Valued Case
263(6)
10.7 Computer Algorithms: Real-Valued Case
269(6)
10.8 Problems and Exercises
275(4)
11 Prediction Theory for Stationary Random Signals
279(12)
11.1 The Wold Decomposition Theorem and Optimal Predictors
279(3)
11.2 Application of the Spectral Representation to the Solution of the Prediction Problem
282(5)
11.3 Examples of Linear Prediction for Stationary Time Series
287(2)
11.4 Problems and Exercises
289(2)
Solutions to Selected Problems and Exercises 291(32)
Bibliographical Comments 323(4)
Index 327
Wojbor A. Woyczyski is a Professor in the Department of Statistics and the Director of the Center for Stochastic and Chaotic Processes in Science and Technology at Case Western Reserve University. His research interests include probability theory, Lévy stochastic processes, random fields and their statistics, nonlinear, stochastic and fractional evolution equations, harmonic and functional analysis, random graphs, statistical physics and hydrodynamics, chaotic dynamics, applications to chemistry, physics, operations research, financial mathematics, medicine, oceanography, and atmospheric physics.