Understanding Digital Signal Processing with MATLAB® and Solutions

The book discusses receiving signals that most electrical engineers detect and study. The vast majority of signals could never be detected due to random additive signals, known as noise, that distorts them or completely overshadows them. Such examples include an audio signal of the pilot communicating with the ground over the engine noise or a bioengineer listening for a fetus’ heartbeat over the mother’s. The text presents the methods for extracting the desired signals from the noise. Each new development includes examples and exercises that use MATLAB to provide the answer in graphic forms for the reader's comprehension and understanding.

CHAPTER 1: CONTINUOUS AND DETERMINISTIC SIGNALS 1.1 Continuous Deterministic Signals 1.2 Sampling of Continuous Signals-Discrete Signals 1.3 Signal conditioning and manipulation 1.4 Convolution of analog and discrete signals 1.5 MATLAB use for vectors and arrays (matrices) CHAPTER 2: FOURIER ANALYSIS OF CONTINUOUS AND DISCRETE SIGNALS 2.1 Introduction 2.2 Fourier transform (FT) of deterministic signals 2.3 Sampling of signals 2.4 Discrete time Fourier transform (DTFT) 2.5 DTFT of finite-time sequences 2.6 The discrete Fourier transform (DFT) Appendix 2.1 Fourier transform properties Appendix 2.2 Fourier transform pairs Appendix 2.3 DTFT properties Appendix 2.4 DFT properties CHAPTER 3: THE Z-TRANSFORM, DIFFERENCE EQUATIONS AND DISCRETE SYSTEMS 3.1 The z-transform 3.2 Properties of the z-transform 3.3 Inverse z-transform 3.4 Transfer function 3.5 Frequency response of discrete systems 3.6 Z-transform solution of difference equations CHAPTER 4: DIGITAL FILTER DESIGN 4.1 Introduction 4.2 Finite impulse response (FIR) filter Appendix 4.1: Window characteristics and performance CHAPTER 5: RANDOM VARIABLES, SEQUENCIES AND PROBABILITY FUNCTIONS 5.1 Random signals and distributions 5.2 Averages 5.3 Stationary processes 5.4 Probability density functions 5.5 Transformations of PDF’s CHAPTER 6: LINEAR SYSTEMS WITH RANDOM INPUTS, FILTERING POWER SPECTRAL DENSITY 6.1 Spectral representation 6.2 Linear systems with random inputs 6.3 Autoregressive moving average processes 6.4 Autoregressive (AR) process 6.5 Parametric representations of stochastic processes: ARMA and ARMAX models CHAPTER 7: LEAST SQUARES-OPTIMUM FILTERING 7.1 Introduction 7.2 The least squares approach 7.3 linear least squares 7.3.1 Matrix formulation of linear least squares 7.4 Point estimation 7.5 Mean square error (MSE) 7.6 Finite impulse response (FIR) Wiener filter 7.7 Wiener solution----Orthogonal principle 7.8 Wiener filtering examples CHAPTER 8: NONPARAMETRIC (CLASSICAL) SPECTRA ESTIMATION 8.1 Periodogram and correlogram spectra estimation 8.2 Book proposed method for better resolution using transformation of the random variables 8.3 Daniel periodogram 8.4 Bartlett periodogram 8.5 Blackman-Tukey (BT) method 8.6 Welch method Appendix 8.1: Important window and their spectra CHAPTER 9: PARAMETRIC AND OTHER METHODS FOR SPECTRA ESTIMATION 9.1 Introduction 9.2 AR, MA and ARMA models 9.3 Yule-Walker (YW) equations 9.4 Least-squares (LS) method and linear prediction 9.5 Minimum variance 9.6 Model order 9.7 Levinson-Durbin algorithm 9.8 Maximum entropy method 9.9 spectrums of segmented signals 9.10 Eigenvalues and eigenvectors of matrices (see also Appendix 2) CHAPTER 10: NEWTON’S AND STEEPEST DESCENT METHODS 10.1 Geometric properties of the error surface 10.2 One-dimensional gradient search method 10.3 Steepest descent algorithm 10.4 Newton’s method 10.5 Solution of the vector difference equation CHAPTER 11: THE LEAST MEAN-SQUARE (LMS) ALGORITHM 11.1 Introduction 11.2 The LMS algorithm 11.3 Examples using the LMS algorithm 11.4 *Performance analysis of the LMS algorithm 11.5 *Complex representation of the LMS algorithm CHAPTER 12: VARIANTS OF LEST MEAN-SQUARE ALGORITHM 12.1 The Normalized Least Mean-Square Algorithm 12.2 Power Normalized LMS 12.3 Self-Correction LMS Filter 12.4 The Sign-Error LMS Algorithm 12.5 The NLMS Sign-Error Algorithm 12.6 The Sign-Regressor LMS Algorithm 12.7 Self-Correcting Sign-Regressor LMS Algorithm 12.8 The Normalized Sign-Regressor LMS Algorithm 12.9 The Sign-Sign LMS Algorithm 12.10 The normalized Sign-Sign LMS Algorithm 12.11 Variable Step-Size LMS Algorithm 12.12 The Leaky LMS Algorithm 12.13 The Linearly Constrained LMS Algorithm 12.14 The Least Mean Fourth Algorithm 12.15 The Least Mean Mixed Normal (LMMN) LMS Algorithm 12.16 Short-Length Signal of the LMS Algorithm 12.17 The Transform Domain LMS Algorithm 12.18 The Error Normalized Step-Size LMS Algorithm 12.19 The Robust Variable Step-Size LMS Algorithm 12.20 The Modified LMS Algorithm 12.21 Momentum LMS Algorithm 12.22 The Block LMS Algorithm 12.23 The Complex LMS Algorithm 12.24 The Affine LMS Algorithm 12.25 The Complex Affine LMS Algorithm CHAPTER 13: NONLINEAR FILTERING 13.1 Introduction 13.2 Statistical Preliminaries 13.3 Mean Filter 13.4 Median Filter 13.5 Trimmed-Type Mean Filter 13.6 L-Filters 13.7 Ranked-Order Statistic Filter 13.8 Edge-Enhancement Filters 13.9 R-Filters APPENDICES Appendix 1: Suggestions and explanations for MATLAB use Appendix 2: MATLAB functions Appendix 3: Mathematical formulas Appendix 4: Langrange multiplier method Appendix 5: Matrix analysis

Dr. Poularikas previously held the positions of Professor at University of Rhode Island, Kingston, USA, Chairman of the Engineering Department at the University of Denver, Colorado, USA, and Chairman of the Electrical and Computer Engineering Department at the University of Alabama in Huntsville, USA. He has published, coauthored, and edited 14 books and served as an editor-in-chief of numerous book series. A Fulbright scholar, lifelong senior member of the IEEE, and member of Tau Beta Pi, Sigma Nu, and Sigma Pi, he received the IEEE Outstanding Educators Award, Huntsville Section in both 1990 and 1996. Dr. Poularikas holds a Ph.D from the University of Arkansas, Fayetteville, USA.