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源码名称：数字信号处理在matlab中的应用(英文版)
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开发语言：MATLAB
更新时间：2021-11-04
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源码介绍
Understanding Digital Signal Processing with MATLAB® and Solutions. by Poularikas, Alexander D.
Understanding Digital Signal Processing with MATLAB® and Solutions. by Poularikas, Alexander D.
Contents Abbreviations................................................................................................................................. xiii Author ..............................................................................................................................................xv Chapter 1 Continuous and Discrete Signals .................................................................................1 1.1 Continuous Deterministic Signals.....................................................................1 Periodic Signals.................................................................................................1 Non-Periodic Continuous Signals .....................................................................1 Unit Step Functions..............................................................................2 Ramp Function .....................................................................................3 Rectangular Function ...........................................................................3 Triangular Pulse Function ....................................................................3 Signum Function ..................................................................................3 Sinc Function........................................................................................3 Gaussian Function ................................................................................3 Error Function ......................................................................................3 Exponential and Double Exponential Functions..................................4 Type of Signals—Even, Odd, Energy and Power.................................4 1.2 Sampling of Continuous Signals-Discrete Signals............................................6 Table 1.1: Some Useful Functions in Analog and Discrete Forms....................7 Approximation of the Derivative and Integral...................................................8 Impulse (delta) Function....................................................................................9 Table 1.2: Basic Delta Function Properties..................................................... 10 The Comb Function......................................................................................... 11 1.3 Signal Conditioning and Manipulation ........................................................... 11 Modulation ......................................................................................... 11 Shifting and Flipping.......................................................................... 12 Time Scaling....................................................................................... 12 Windowing of Signals........................................................................ 12 Table 1.3: Windows for Continuous Signal Processing................................... 12 1.4 Convolution of Analog and Discrete Signals .................................................. 13 Analog Signals ................................................................................... 13 Discrete Signals.................................................................................. 13 Table 1.4: Basic Convolution Properties ......................................................... 16 1.5 MATLAB Use for Vectors and Arrays (Matrices).......................................... 17 Examples of Array Operations........................................................... 17 Hints–Suggestions–Solutions of the Exercises .......................................................... 18 Chapter 2 Fourier Analysis of Continuous and Discrete Signals ............................................... 21 2.1 Introduction ..................................................................................................... 21 2.2 Fourier Transform (FT) of Deterministic Signals........................................... 21 2.3 Sampling of Signals.........................................................................................24 2.4 Discrete-Time Fourier Transform (DTFT)......................................................27 2.5 DTFT of Finite-Time Sequences.....................................................................30 Windowing ......................................................................................... 32 2.6 The Discrete Fourier Transform (DFT) .......................................................... 33 The Inverse DFT (IDFT) .................................................................................34 viii Contents 2.7 Properties of DFT............................................................................................34 Linearity..............................................................................................34 Symmetry ...........................................................................................34 Time Shifting...................................................................................... 35 Frequency Shifting ............................................................................. 35 Time Convolution............................................................................... 35 Frequency Convolution ......................................................................37 Parseval’s Theorem.............................................................................37 2.8 Effect of Sampling Time T..............................................................................37 2.9 Effect of Truncation.........................................................................................39 Windowing .........................................................................................40 2.10 Resolution........................................................................................................40 2.11 Discrete Systems ............................................................................................. 41 2.12 Digital Simulation of Analog Systems............................................................46 2.12.1 Second-Order Differential Equations ................................................ 52 Hints–Suggestions–Solutions of the Exercises ..........................................................54 Appendix 2.1: Fourier Transform Properties ............................................................. 61 Appendix 2.2: Fourier Transform Pairs...................................................................... 62 Appendix 2.3: DTFT Properties.................................................................................63 Appendix 2.4: DFT Properties...................................................................................64 Chapter 3 The z-Transform, Difference Equations, and Discrete Systems .................................65 3.1 The z-Transform...............................................................................................65 3.2 Properties of the z-Transform.......................................................................... 67 Table 3.1: Summary of z-Transform Properties......................................................... 67 3.3 Inverse z-Transform ......................................................................................... 73 Table 3.2: Common z-Transform Pairs....................................................................... 74 3.4 Transfer Function.............................................................................................77 Higher-Order Transfer Functions...............................................................................79 3.5 Frequency Response of Discrete Systems.......................................................80 3.6 z-Transform Solution of Difference Equations................................................82 Hints–Suggestions–Solutions of the Exercises ..........................................................84 Chapter 4 Finite Impulse Response (FIR) Digital Filter Design ................................................89 4.1 Introduction .....................................................................................................89 4.2 Finite Impulse Response (FIR) Filters............................................................89 Discrete Fourier-Series Method .........................................................89 Commonly Used Windows.................................................................94 Discrete Fourier Transform Method...................................................95 High-Pass Filter..................................................................................96 Table 4.1: Frequency Transformations.......................................................................98 Hints–Suggestions–Solutions of the Exercises ........................................................100 Appendix 4.1: Window Characteristics and Performance........................................ 103 Chapter 5 Random Variables, Sequences, and Probability Functions ...................................... 105 5.1 Random Signals and Distributions................................................................ 105 Stochastic Processes......................................................................... 110 Stationary and Ergodic Processes..................................................... 111 5.2 Averages ........................................................................................................ 112 Contents ix Mean Value....................................................................................... 112 Correlation........................................................................................ 113 Sample Autocorrelation Function..................................................... 113 Covariance........................................................................................ 115 Independent and Uncorrelated RVs.................................................. 116 5.3 Stationary Processes...................................................................................... 116 Table 5.1: Properties of WSS Processes........................................................ 117 Autocorrelation Matrix..................................................................... 117 Purely Random Process (WN) ......................................................... 118 Random Walk (RW) ......................................................................... 119 5.4 Probability Density Functions....................................................................... 119 Uniform Distribution........................................................................ 119 Table 5.2: Properties and Definitions ............................................................120 Gaussian (Normal) Distribution ....................................................... 121 Table 5.3: Properties of a Gaussian Random Process ................................... 121 Exponential Distribution ..................................................................124 Lognormal Distribution....................................................................126 Chi-Square Distribution ...................................................................126 Student’s Distribution....................................................................... 127 F Distribution ................................................................................... 128 Rayleigh Probability Density Function ............................................128 5.5 Transformations of PDFs............................................................................... 130 Hints, Suggestions, and Solutions for the Exercises................................................ 132 Chapter 6 Linear Systems with Random Inputs, Filtering, and Power Spectral Density ......... 137 6.1 Spectral Representation................................................................................. 137 The Wiener–Khintchine (W–K) Relations.................................................... 139 6.2 Linear Systems with Random Inputs ............................................................ 142 Table 6.1: Summary of Correlation and Spectral Densities .......................... 143 6.3 Autoregressive Moving Average Processes (ARMA) ................................... 149 6.4 Autoregressive (AR) Process......................................................................... 151 *6.5 Parametric Representations of Stochastic Processes: ARMA and ARMAX Models........................................................................................... 154 Table 6.2: Linear Systems and Random Signals...................................................... 154 Table 6.3: ARMAX Representation ......................................................................... 159 Table 6.4: MA Representation.................................................................................. 160 Table 6.5: AR Representation................................................................................... 160 Hints–Suggestions–Solutions for the Exercises....................................................... 161 Chapter 7 Least Squares-Optimum Filtering............................................................................ 167 7.1 Introduction ................................................................................................... 167 7.2 The Least-Squares Approach ........................................................................ 167 7.3 Linear Least Squares..................................................................................... 170 *7.3.1 Matrix Formulation of Linear Least Squares (LLS)........................ 171 7.4 Point Estimation ............................................................................................ 172 7.4.1 Estimator Performance..................................................................... 173 7.4.2 Biased and Unbiased Estimators...................................................... 175 7.4.3 Cramer–Rao Lower Bound (CRLB) ................................................ 175 7.4.4 Mean Square Error Criterion ........................................................... 178 7.4.5 Maximum Likelihood Estimator...................................................... 178 x Contents 7.5 Mean Square Error (MSE) ............................................................................ 184 7.6 Finite Impulse Response (FIR) Wiener Filter............................................... 186 7.7 Wiener Solution—Orthogonal Principle....................................................... 190 7.7.1 Orthogonality Condition .................................................................. 193 7.8 Wiener Filtering Examples............................................................................ 193 7.8.1 Linear Prediction..............................................................................204 Hints, Suggestions, and Solutions of the Exercises..................................................205 Chapter 8 Nonparametric (Classical) Spectra Estimation ........................................................ 211 8.1 Periodogram and Correlogram Spectra Estimation ...................................... 211 8.1.1 Deterministic Signals (see also Chapter 2) ...................................... 211 8.1.2 The Periodogram-Random Signals.................................................. 212 8.1.3 Correlogram ..................................................................................... 214 8.1.4 Computation of Periodogram and Correlogram Using FFT............ 215 Windowed Periodogram ................................................................................ 221 8.2 Book Proposed Method for Better Resolution Using Transformation of the Random Variables ...................................................................................222 8.3 Daniel Periodogram.......................................................................................223 8.4 Bartlett Periodogram.....................................................................................224 8.4.1 Book-Modified Method....................................................................226 8.5 Blackman–Tukey (BT) Method.....................................................................229 8.6 Welch Method................................................................................................ 233 8.6.1 Proposed Modified Methods for Welch Method.............................. 235 Modified Method Using Different Types of Overlapping ................ 235 Modified Welch Method Using RV Transformation ........................238 Hints, Suggestions, and Solutions of the Exercises.................................................. 239 Appendix A8.1: Important Windows and Their Spectra .......................................... 241 Chapter 9 Parametric and Other Methods for Spectral Estimation ..........................................245 9.1 Introduction ...................................................................................................245 9.2 AR, MA, and ARMA Models.......................................................................245 9.3 Yule–Walker (YW) Equations......................................................................247 9.4 Least-Squares (LS) Method and Linear Prediction ...................................... 251 9.5 Minimum Variance Method..........................................................................254 9.6 Model Order ..................................................................................................256 9.7 Levinson–Durbin Algorithm......................................................................... 257 9.8 Maximum Entropy Method...........................................................................262 9.9 Spectrums of Segmented Signals..................................................................263 9.9.1 Method 1: The Average Method.......................................................264 9.9.2 Method 2: Extrapolation Method .....................................................265 9.10 Eigenvalues and Eigenvectors of Matrices (See Also Appendix 2) ..............268 9.10.1 Eigendecomposition of the Autocorrelation Matrix.........................269 Table 9.1: Eigenvalue Properties................................................................... 270 9.10.2 Harmonic Model .............................................................................. 273 9.10.3 Pisarenko Harmonic Decomposition ...............................................277 9.10.4 MUSIC Algorithm............................................................................ 278 Hints, Suggestions, and Solutions of the Exercises.................................................. 279 Contents xi Chapter 10 Newton’s and Steepest Descent Methods .................................................................285 10.1 Geometric Properties of the Error Surface ...................................................285 10.2 One-Dimensional Gradient Search Method..................................................288 10.2.1 Gradient Search Algorithm..............................................................289 10.2.2 Newton’s Method in Gradient Search ..............................................290 10.3 Steepest Descent Algorithm.......................................................................... 291 10.3.1 Steepest Descent Algorithm Applied to Wiener Filter ....................292 10.3.2 Stability (Convergence) of the Algorithm ........................................294 10.3.3 Transient Behavior of MSE..............................................................295 10.3.4 Learning Curve ................................................................................297 10.4 Newton’s Method...........................................................................................297 *10.5 Solution of the Vector Difference Equation ..................................................299 Additional Exercises.................................................................................................302 Hints, Suggestions, and Solutions of the Exercises..................................................302 Chapter 11 The Least Mean Square (LMS) Algorithm ..............................................................307 11.1 Introduction ...................................................................................................307 11.2 The LMS Algorithm......................................................................................307 Table 11.2.1: The LMS Algorithm for an Mth-Order FIR Filter..............................309 11.3 Example Using the LMS Algorithm ............................................................. 310 *11.4 Performance Analysis of the LMS Algorithm .............................................. 318 11.4.1 Learning Curve ................................................................................320 11.4.2 The Coefficient-Error or Weighted-Error Correlation Matrix ......... 322 11.4.3 Excess MSE and Misadjustment ......................................................324 11.4.4 Stability ............................................................................................ 326 11.4.5 The LMS and Steepest-Descent Method.......................................... 327 *11.5 Complex Representation of the LMS Algorithm .......................................... 327 Hints, Suggestions, and Solutions of the Exercises.................................................. 330 Chapter 12 Variants of Least Mean Square Algorithm .............................................................. 333 12.1 The Normalized Least Mean Square Algorithm........................................... 333 Table 12.1: Some Variants of the LMS Formulas..................................................... 334 Table 12.2: Normalized Real and Complex LMS Algorithms................................. 334 12.2 Power NLMS................................................................................................. 337 12.3 Self-Correcting LMS Filter........................................................................... 341 12.4 The Sign-Error LMS Algorithm.................................................................... 342 12.5 The NLMS Sign-Error Algorithm................................................................. 343 12.6 The Sign-Regressor LMS Algorithm ............................................................344 12.7 Self-Correcting Sign-Regressor LMS Algorithm .........................................345 12.8 The Normalized Sign-Regressor LMS Algorithm........................................346 12.9 The Sign–Sign LMS Algorithm.................................................................... 347 12.10 The Normalized Sign–Sign LMS Algorithm................................................349 12.11 Variable Step-Size LMS................................................................................ 350 Table 12.3: The VSLMS Algorithm ......................................................................... 351 12.12 The Leaky LMS Algorithm .......................................................................... 352 12.13 The Linearly Constrained LMS Algorithm................................................... 354 Table 12.4: Linearly Constrained LMS Algorithm .................................................. 357 xii Contents 12.14 The Least Mean Fourth Algorithm ............................................................... 358 12.15 The Least Mean Mixed Normal (LMMN) LMS Algorithm ........................ 358 12.16 Short-Length Signal of the LMS Algorithm ................................................. 359 12.17 The Transform Domain LMS Algorithm......................................................360 *12.17.1 Convergence ................................................................................. 363 12.18 The Error Normalized Step-Size LMS Algorithm........................................364 12.19 The Robust Variable Step-Size LMS Algorithm...........................................368 12.20 The Modified LMS Algorithm...................................................................... 372 12.21 Momentum LMS Algorithm ......................................................................... 373 12.22 The Block LMS Algorithm ........................................................................... 374 12.23 The Complex LMS Algorithm ...................................................................... 375 Table 12.5: Complex LMS Algorithm...................................................................... 375 12.24 The Affine LMS Algorithm .......................................................................... 377 Table 12.6: The Affine Projection Algorithm........................................................... 378 12.25 The Complex Affine LMS Algorithm........................................................... 379 Table 12.7: Complex Affine Algorithm.................................................................... 379 Hints, Solutions, and Suggestions of the Exercises..................................................380 Chapter 13 Nonlinear Filtering ................................................................................................... 385 13.1 Introduction ................................................................................................... 385 13.2 Statistical Preliminaries................................................................................. 385 13.2.1 Signal and Noise Model-Robustness............................................... 385 13.2.2 Point Estimation ..............................................................................386 13.2.3 Estimator Performance ....................................................................386 13.2.4 Biased and Unbiased Estimator.......................................................388 13.2.5 Cramer–Rao Lower Bound..............................................................388 13.2.6 Mean Square Error Criterion...........................................................390 13.2.7 Maximum Likelihood Estimator .....................................................390 13.3 Mean Filter....................................................................................................396 13.4 Median Filter................................................................................................. 398 13.5 Trimmed-Type Mean Filter ...........................................................................400 13.5.1 (r−s)-Fold Trimmed Mean Filters...................................................400 13.5.2 (r,s)-Fold Winsorized Mean Filter...................................................403 13.5.3 Alpha-Trimmed Mean Filter and Alpha-Winsorized Mean Filter...403 13.5.4 Alpha-Trimmed Winsorized Mean Filter.........................................404 13.6 L-Filters.........................................................................................................405 13.7 Rank-Order Statistic Filter ............................................................................406 13.8 Edge-Enhancement Filters ............................................................................408 13.9 R-Filters.........................................................................................................409 Additional Exercises................................................................................................. 411 Problems, Solutions, Suggestions, and Hints........................................................... 411 Appendix 1: Suggestions and Explanations for MATLAB Use............................................... 415 Appendix 2: Matrix Analysis ......................................................................................................427 Appendix 3: Mathematical Formulas ........................................................................................437 Appendix 4: MATLAB Functions ..............................................................................................443 Bibliography .................................................................................................................................447 Index .......................... 449