Statistical Signal Processing in Engineering

A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students
 
This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals. In writing it, the author drew on his vast theoretical and practical experience in the field to provide a quick-solution manual for technicians and engineers, offering field-tested solutions to most problems engineers can encounter. At the same time, the book delineates the basic concepts and applied mathematics underlying each solution so that readers can go deeper into the theory to gain a better idea of the solution's limitations and potential pitfalls, and thus tailor the best solution for the specific engineering application.
 
Uniquely, Statistical Signal Processing in Engineering can also function as a textbook for engineering graduates and post-graduates. Dr. Spagnolini, who has had a quarter of a century of experience teaching graduate-level courses in digital and statistical signal processing methods, provides a detailed axiomatic presentation of the conceptual and mathematical foundations of statistical signal processing that will challenge students' analytical skills and motivate them to develop new applications on their own, or better understand the motivation underlining the existing solutions.
 
Throughout the book, some real-world examples demonstrate how powerful a tool statistical signal processing is in practice across a wide range of applications.
* Takes an interdisciplinary approach, integrating basic concepts and tools for statistical signal processing
* Informed by its author's vast experience as both a practitioner and teacher
* Offers a hands-on approach to solving problems in statistical signal processing
* Covers a broad range of applications, including communication systems, machine learning, wavefield and array processing, remote sensing, image filtering and distributed computations
* Features numerous real-world examples from a wide range of applications showing the mathematical concepts involved in practice
* Includes MATLAB code of many of the experiments in the book
 
Statistical Signal Processing in Engineering is an indispensable working resource for electrical engineers, especially those working in the information and communication technology (ICT) industry. It is also an ideal text for engineering students at large, applied mathematics post-graduates and advanced undergraduates in electrical engineering, applied statistics, and pure mathematics, studying statistical signal processing.

List of contents

List of Figures xvii
 
List of Tables xxiii
 
Preface xxv
 
List of Abbreviations xxix
 
How to Use the Book xxxi
 
About the Companion Website xxxiii
 
Prerequisites xxxv
 
Why are there so many matrixes in this book? xxxvii
 
1 Manipulations on Matrixes 1
 
1.1 Matrix Properties 1
 
1.1.1 Elementary Operations 2
 
1.2 Eigen-Decomposition 6
 
1.3 Eigenvectors in Everyday Life 9
 
1.3.1 Conversations in a Noisy Restaurant 9
 
1.3.2 Power Control in a Cellular System 12
 
1.3.3 Price Equilibrium in the Economy 14
 
1.4 Derivative Rules 15
 
1.4.1 Derivative with respect to x 16
 
1.4.2 Derivative with respect to x 17
 
1.4.3 Derivative with respect to the Matrix X 18
 
1.5 Quadratic Forms 19
 
1.6 Diagonalization of a Quadratic Form 20
 
1.7 Rayleigh Quotient 21
 
1.8 Basics of Optimization 22
 
1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23
 
1.8.2 Quadratic Function with Multiple Linear Constraints 23
 
Appendix A: Arithmetic vs. Geometric Mean 24
 
2 Linear Algebraic Systems 27
 
2.1 Problem Definition and Vector Spaces 27
 
2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29
 
2.2 Rotations 31
 
2.3 Projection Matrixes and Data-Filtering 33
 
2.3.1 Projections and Commercial FM Radio 34
 
2.4 Singular Value Decomposition (SVD) and Subspaces 34
 
2.4.1 How to Choose the Rank of Afor Gaussian Model? 35
 
2.5 QR and Cholesky Factorization 36
 
2.6 Power Method for Leading Eigenvectors 38
 
2.7 Least Squares Solution of Overdetermined Linear Equations 39
 
2.8 Efficient Implementation of the LS Solution 41
 
2.9 Iterative Methods 42
 
3 Random Variables in Brief 45
 
3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45
 
3.2 Convexity and Jensen Inequality 49
 
3.3 Uncorrelatedness and Statistical Independence 49
 
3.4 Real-Valued Gaussian Random Variables 51
 
3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54
 
3.6 Conditional pdf in Additive Noise Model 56
 
3.7 Complex Gaussian Random Variables 56
 
3.7.1 Single Complex Gaussian Random Variable 56
 
3.7.2 Circular Complex Gaussian Random Variable 57
 
3.7.3 Multivariate Complex Gaussian Random Variables 58
 
3.8 Sum of Square of Gaussians: Chi-Square 59
 
3.9 Order Statistics for N rvs 60
 
4 Random Processes and Linear Systems 63
 
4.1 Moment Characterizations and Stationarity 64
 
4.2 Random Processes and Linear Systems 66
 
4.3 Complex-Valued Random Processes 68
 
4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69
 
4.4.1 Stability of LTI Systems 70
 
4.4.2 Rational PSD 71
 
4.4.3 Paley-Wiener Theorem 72
 
4.5 Gaussian Random Process (Discrete-Time) 73
 
4.6 Measuring Moments in Stochastic Processes 75
 
Appendix A: Transforms for Continuous-Time Signals 76
 
Appendix B: Transforms for Discrete-Time Signals 79
 
5 Models and Applications 83
 
5.1 Linear Regression Model 84
 
5.2 Linear Filtering Model 86
 
5.2.1 Block-Wise Circular Convolution 88
 
5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89
 
5.2.3 Identification and Deconvolution 90
 
5.3 MIMO systems and Interference Models 91
 
5.3.1 DSL System 92
 
5.3.2 MIMO in Wireless Communication 92
 
5.4 Sinusoidal Signal 97
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About the author

UMBERTO SPAGNOLINI is Professor in Signal Processing and Telecommunications at Politecnico di Milano, Italy. Prof. Spagnolini's research focuses on statistical signal processing, communication systems, and advanced topics in signal processing for remote sensing and wireless communication systems. He is a Senior Member of the IEEE, engages in editorial activity for IEEE journals and conferences, and has authored 300 patents and papers in peer reviewed journals and conferences.

Summary

A problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals.

Product details

• Authors: U Spagnolini, Umberto Spagnolini
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 31.12.2017
• EAN: 9781119293972
• ISBN: 978-1-119-29397-2
• No. of pages: 608
• Subjects: Natural sciences, medicine, IT, technology > Technology > Electronics, electrical engineering, communications engineering; Statistik, Statistics, Signalverarbeitung, Signal Processing, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Statistik in den Ingenieurwissenschaften, Engineering Statistics