2nd Edition

# Digital Signal Processing with Examples in MATLAB®

By Samuel D. Stearns, Donald R. Hush Copyright 2011
510 Pages 268 B/W Illustrations
by CRC Press

516 Pages
by CRC Press

Also available as eBook on:

Based on fundamental principles from mathematics, linear systems, and signal analysis, digital signal processing (DSP) algorithms are useful for extracting information from signals collected all around us. Combined with today’s powerful computing capabilities, they can be used in a wide range of application areas, including engineering, communications, geophysics, computer science, information technology, medicine, and biometrics.

Updated and expanded, Digital Signal Processing with Examples in MATLAB®, Second Edition introduces the basic aspects of signal processing and presents the fundamentals of DSP. It also relates DSP to continuous signal processing, rather than treating it as an isolated operation.

New to the Second Edition

• Discussion of current DSP applications
• New chapters on analog systems models and pattern recognition using support vector machines
• New sections on the chirp z-transform, resampling, waveform reconstruction, discrete sine transform, and logarithmic and nonuniform sampling
• A more comprehensive table of transforms

Developing the fundamentals of DSP from the ground up, this bestselling text continues to provide readers with a solid foundation for further work in most areas of signal processing. For novices, the authors review the basic mathematics required to understand DSP systems and offer a brief introduction to MATLAB. They also include end-of-chapter exercises that not only provide examples of the topics discussed, but also introduce topics and applications not covered in the chapters.

Introduction
Digital Signal Processing (DSP)
Introduction to MATLAB
Signals, Vectors, and Arrays
Review of Vector and Matrix Algebra Using MATLAB Notation
Geometric Series and Other Formulas
MATLAB Functions in DSP

Least Squares, Orthogonality, and the Fourier Series
Introduction
Least Squares
Orthogonality
Discrete Fourier Series

Correlation, Fourier Spectra, and the Sampling Theorem
Introduction
Correlation
The Discrete Fourier Transform (DFT)
Redundancy in the DFT
The Fast Fourier Transform (FFT) Algorithm
Amplitude and Phase Spectra
The Inverse DFT
Properties of the DFT
Continuous Transforms, Linear Systems, and Convolution
The Sampling Theorem
Waveform Reconstruction and Aliasing
Resampling
Nonuniform and Log-Spaced Sampling

Linear Systems and Transfer Functions
Continuous and Discrete Linear Systems
Properties of Discrete Linear Systems
Discrete Convolution
The z-Transform and Linear Transfer Functions
The Complex Z-Plane and the Chirp z-Transform
Poles and Zeros
Transient Response and Stability
System Response via the Inverse z-Transform
Direct Algorithms
State-Space Algorithms
Lattice Algorithms and Structures
FFT Algorithms
Discrete Linear Systems and Digital Filters
Functions Used in This Chapter

Finite Impulse Response Filter Design
Introduction
An Ideal Lowpass Filter
The Realizable Version
Improving a Finite Impulse Response (FIR) Filter with Window Functions
Highpass, Bandpass, and Bandstop Filters
A Complete FIR Filtering Example
Other Types of FIR Filters
Digital Differentiation
A Hilbert Transformer

Infinite Impulse Response Filter Design
Introduction
Linear Phase
Butterworth Filters
Chebyshev Filters
Frequency Translations
The Bilinear Transformation
Infinite Impulse Response (IIR) Digital Filters
Digital Resonators and the Spectrogram
The All-Pass Filter
Digital Integration and Averaging

Random Signals and Spectral Estimation
Introduction
Amplitude Distributions
Uniform, Gaussian, and Other Distributions
Power and Power Density Spectra
Properties of the Power Spectrum
Power Spectral Estimation
Data Windows in Spectral Estimation
The Cross-Power Spectrum
Algorithms

Least-Squares System Design
Introduction
Applications of Least-Squares Design
System Design via the Mean-Squared Error
A Design Example
Least-Squares Design with Finite Signal Vectors
Correlation and Covariance Computation
Channel Equalization
System Identification
Interference Canceling
Linear Prediction and Recovery

Introduction
The Mean-Squared Error Performance Surface
Searching the Performance Surface
Steepest Descent and the Least-Mean-Square (LMS) Algorithm
LMS Examples
Direct Descent and the Recursive-Least-Squares (RLS) Algorithm

Signal Information, Coding, and Compression
Introduction
Measuring Information
Two Ways to Compress Signals
Entropy Coding
Transform Coding and the Discrete Cosine Transform
The Discrete Sine Transform
Multirate Signal Decomposition and Subband Coding
Time–Frequency Analysis and Wavelet Transforms

Models of Analog Systems
Introduction
Impulse-Invariant Approximation
Final Value Theorems
Pole–Zero Comparisons
Approaches to Modeling
Input-Invariant Models
Other Linear Models
Comparison of Linear Models
Models of Multiple and Nonlinear Systems
Concluding Remarks

Pattern Recognition with Support Vector Machines
Introduction
Pattern Recognition Principles
Learning
Support Vector Machines
Multiclass Classification
MATLAB Examples

Appendix: Table of Laplace and Z-Transforms

Index

Exercises and References appear at the end of each chapter.

### Biography

Samuel D. Stearns is a professor emeritus at the University of New Mexico, where has been involved in adjunct teaching and research since 1960. An IEEE fellow, Dr. Stearns was also a distinguished member of the technical staff at Sandia National Laboratories for 27 years. His principal technical areas are DSP and adaptive signal processing.

Don R. Hush is a technical staff member at the Los Alamos National Laboratory. An IEEE senior member, Dr. Hush was previously a technical staff member at Sandia National Laboratories and a professor at the University of New Mexico. He was also an associate editor for IEEE Transactions on Neural Networks and IEEE Signal Processing Magazine.

"This book will guide you through the mathematics and electrical engineering theory using real-world applications. It will also use MATLAB®, a software tool that allows you to easily implement signal-processing techniques using the computer and to view the signals graphically. … The reader of this text is fortunate to be guided by two wonderful teachers who translate the issues and understanding of using signal processing in the real world to examples and applications that open the door to this fascinating subject."
—From the Foreword by Dr. Delores M. Etter, Texas Instruments Distinguished Chair in Engineering Education and director of the Caruth Institute for Engineering Education, Southern Methodist University, Dallas, Texas, USA

Praise for the First Edition
In a field as rapidly expanding as digital signal processing (DSP), even the basic topics change over time, both in nature and relative importance. It is important, therefore, to have an up-to-date text that not only covers the fundamentals but also follows a logical development that leaves no gaps that readers must somehow bridge by themselves. Digital Signal Processing with Examples in MATLAB is such a text.
IEEE Signal Processing Magazine, Vol. 22, No. 4, July 2005

It is a pleasure to recommend this book to the serious student of digital signal processing. It is carefully written and illustrated by many useful examples and exercises, and the material is selected to cover the relevant topics in this rapidly developing field of knowledge.
—the late Professor Richard W. Hamming, Bell Laboratories