Discrete Random Signal Processing and Filtering Primer with MATLAB

Alexander D. Poularikas

• Publisher: CRC Press
• Year: 2018
• Print ISBN: 9781420089332
• eBook ISBN: 9781351834452
• Topic: Technology & Engineering
• Subtopic: Electrical Engineering & Telecommunications
• Index: Technology & Engineering

Engineers in all fields will appreciate a practical guide that combines several new effective MATLAB® problem-solving approaches and the very latest in discrete random signal processing and filtering.
Numerous Useful Examples, Problems, and Solutions – An Extensive and Powerful Review
Written for practicing engineers seeking to strengthen their practical grasp of random signal processing, Discrete Random Signal Processing and Filtering Primer with MATLAB provides the opportunity to doubly enhance their skills. The author, a leading expert in the field of electrical and computer engineering, offers a solid review of recent developments in discrete signal processing. The book also details the latest progress in the revolutionary MATLAB language.
A Practical Self-Tutorial That Transcends TheoryThe author introduces an incremental discussion of signal processing and filtering, and presents several new methods that can be used for a more dynamic analysis of random digital signals with both linear and non-linear filtering. Ideal as a self-tutorial, this book includes numerous examples and functions, which can be used to select parameters, perform simulations, and analyze results. This concise guide encourages readers to use MATLAB functions – and those new ones introduced as Book MATLAB Functions – to substitute many different combinations of parameters, giving them a firm grasp of how much each parameter affects results.
Much more than a simple review of theory, this book emphasizes problem solving and result analysis, enabling readers to take a hands-on approach to advance their own understanding of MATLAB and the way it is used within signal processing and filtering.

chapter one

Fourier analysis of signals

1.1 Introduction

One of the most fundamental information of any signal is its cyclic or oscillating activity. Our main interest is to determine the sinusoidal components of the signal, the range of their amplitude and frequency values.

Fourier analysis provides us with different tools, which are appropriate for particular type of signals. If the signal is periodic and deterministic, we use Fourier series analysis. If the signal is finite and deterministic, we use the Fourier transform (FT). For discrete time signals the discrete FT (DFT) is used, whereas the random signals need special approaches for their frequency content determination. Figure 1.1 shows a deterministic periodic, a deterministic finite and a random signal.

1.2 Fourier transform (FT)

The FT is used to find the frequency content of those signals that, at least, satisfy the Dirichlet conditions, which are (1) the signal has finite values of its maximum and minimum within a finite interval, (2) the signal has finite number of disco...

Table of contents

• Cover
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Author
• Abbreviations
• Chapter 1 Fourier analysis of signals
• Chapter 2 Random variables, sequences, and stochastic processes
• Chapter 3 Nonparametric (classical) spectra estimation
• Chapter 4 Parametric and other methods for spectra estimation
• Chapter 5 Optimal filtering—Wiener filters
• Chapter 6 Adaptive filtering—LMS algorithm
• Chapter 7 Adaptive filtering with variations of LMS algorithm
• Chapter 8 Nonlinear filtering
• Bibliography
• Appendix A Suggestions and explanations for MATLAB® use
• Appendix B Matrix analysis
• Appendix C Lagrange multiplier method
• Index