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E-raamat: Understanding Digital Signal Processing with MATLAB® and Solutions

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(The University of Alabama in Huntsville, USA)
  • Formaat: 471 pages
  • Ilmumisaeg: 13-Nov-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781351623278
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Understanding Digital Signal Processing with MATLAB® and SolutionsSuurem pilt
  • Formaat: 471 pages
  • Ilmumisaeg: 13-Nov-2017
  • Kirjastus: CRC Press
  • ISBN-13: 9781351623278
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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.

Arvustused

"Timely and fundamental subject, sparking interest for students and engineers alike. Starts from the basics and builds up the complexity in a logic and very understandable way, so that both beginners and experienced professionals will be able to profit from the book. The book is very useful as a reference, with an extensive set of digital processing operations and clear MATLAB examples and proposed exercises for all of them. The reader can easily find everything related to one specific topic (eg. Fourier transform)." Alexandre Giulietti de Barros, Teledyne Anafocus, Spain

"The book deals with methods for processing noisy signals. The contents is fairly complete and covers all important topics ranging from discrete and continuous Fourier processing, digital filtering to random signal processing and nonlinear filtering." -Hans-Georg Stark (Aschaffenburg) "Timely and fundamental subject, sparking interest for students and engineers alike. Starts from the basics and builds up the complexity in a logic and very understandable way, so that both beginners and experienced professionals will be able to profit from the book. The book is very useful as a reference, with an extensive set of digital processing operations and clear MATLAB examples and proposed exercises for all of them. The reader can easily find everything related to one specific topic (eg. Fourier transform)." Alexandre Giulietti de Barros, Teledyne Anafocus, Spain

"The book deals with methods for processing noisy signals. The contents is fairly complete and covers all important topics ranging from discrete and continuous Fourier processing, digital filtering to random signal processing and nonlinear filtering." -Hans-Georg Stark (Aschaffenburg)

Abbreviations xiii
Author xv
Chapter 1 Continuous and Discrete Signals 1(20)
1.1 Continuous Deterministic Signals
1(5)
Periodic Signals
1(1)
Non-Periodic Continuous Signals
1(5)
Unit Step Functions
2(1)
Ramp Function
3(1)
Rectangular Function
3(1)
Triangular Pulse Function
3(1)
Signum Function
3(1)
Sinc Function
3(1)
Gaussian Function
3(1)
Error Function
3(1)
Exponential and Double Exponential Functions
4(1)
Type of Signals-Even, Odd, Energy and Power
4(2)
1.2 Sampling of Continuous Signals-Discrete Signals
6(5)
Table 1.1: Some Useful Functions in Analog and Discrete Forms
7(1)
Approximation of the Derivative and Integral
8(1)
Impulse (delta) Function
9(1)
Table 1.2: Basic Delta Function Properties
10(1)
The Comb Function
11(1)
1.3 Signal Conditioning and Manipulation
11(2)
Modulation
11(1)
Shifting and Flipping
12(1)
Time Scaling
12(1)
Windowing of Signals
12(1)
Table 1.3: Windows for Continuous Signal Processing
12(1)
1.4 Convolution of Analog and Discrete Signals
13(4)
Analog Signals
13(1)
Discrete Signals
13(3)
Table 1.4: Basic Convolution Properties
16(1)
1.5 MATLAB Use for Vectors and Arrays (Matrices)
17(1)
Examples of Array Operations
17(1)
Hints-Suggestions-Solutions of the Exercises
18(3)
Chapter 2 Fourier Analysis of Continuous and Discrete Signals 21(44)
2.1 Introduction
21(1)
2.2 Fourier Transform (FT) of Deterministic Signals
21(3)
2.3 Sampling of Signals
24(3)
2.4 Discrete-Time Fourier Transform (DTFT)
27(3)
2.5 DTFT of Finite-Time Sequences
30(3)
Windowing
32(1)
2.6 The Discrete Fourier Transform (DFT)
33(1)
The Inverse DFT (IDFT)
34(1)
2.7 Properties of DFT
34(3)
Linearity
34(1)
Symmetry
34(1)
Time Shifting
35(1)
Frequency Shifting
35(1)
Time Convolution
35(2)
Frequency Convolution
37(1)
Parseval's Theorem
37(1)
2.8 Effect of Sampling Time T
37(2)
2.9 Effect of Truncation
39(1)
Windowing
40(1)
2.10 Resolution
40(1)
2.11 Discrete Systems
41(5)
2.12 Digital Simulation of Analog Systems
46(8)
2.12.1 Second-Order Differential Equations
52(2)
Hints-Suggestions-Solutions of the Exercises
54(7)
Appendix 2.1: Fourier Transform Properties
61(1)
Appendix 2.2: Fourier Transform Pairs
62(1)
Appendix 2.3: DTFT Properties
63(1)
Appendix 2.4: DFT Properties
64(1)
Chapter 3 The z-Transform, Difference Equations, and Discrete Systems 65(24)
3.1 The z-Transform
65(2)
3.2 Properties of the z-Transform
67(6)
Table 3.1: Summary of z-Transform Properties
67(6)
3.3 Inverse z-Transform
73(4)
Table 3.2: Common z-Transform Pairs
74(3)
3.4 Transfer Function
77(3)
Higher-Order Transfer Functions
79(1)
3.5 Frequency Response of Discrete Systems
80(2)
3.6 z-Transform Solution of Difference Equations
82(2)
Hints-Suggestions-Solutions of the Exercises
84(5)
Chapter 4 Finite Impulse Response (FIR) Digital Filter Design 89(16)
4.1 Introduction
89(1)
4.2 Finite Impulse Response (FIR) Filters
89(11)
Discrete Fourier-Series Method
89(5)
Commonly Used Windows
94(1)
Discrete Fourier Transform Method
95(1)
High-Pass Filter
96(2)
Table 4.1: Frequency Transformations
98(2)
Hints-Suggestions-Solutions of the Exercises
100(3)
Appendix 4.1: Window Characteristics and Performance
103(2)
Chapter 5 Random Variables, Sequences, and Probability Functions 105(32)
5.1 Random Signals and Distributions
105(7)
Stochastic Processes
110(1)
Stationary and Ergodic Processes
111(1)
5.2 Averages
112(4)
Mean Value
112(1)
Correlation
113(1)
Sample Autocorrelation Function
113(2)
Covariance
115(1)
Independent and Uncorrelated RVs
116(1)
5.3 Stationary Processes
116(3)
Table 5.1: Properties of WSS Processes
117(1)
Autocorrelation Matrix
117(1)
Purely Random Process (WN)
118(1)
Random Walk (RW)
119(1)
5.4 Probability Density Functions
119(11)
Uniform Distribution
119(1)
Table 5.2: Properties and Definitions
120(1)
Gaussian (Normal) Distribution
121(1)
Table 5.3: Properties of a Gaussian Random Process
121(3)
Exponential Distribution
124(2)
Lognormal Distribution
126(1)
Chi-Square Distribution
126(1)
Student's Distribution
127(1)
F Distribution
128(1)
Rayleigh Probability Density Function
128(2)
5.5 Transformations of PDFs
130(2)
Hints, Suggestions, and Solutions for the Exercises
132(5)
Chapter 6 Linear Systems with Random Inputs, Filtering, and Power Spectral Density 137(30)
6.1 Spectral Representation
137(5)
The Wiener-Khintchine (W-K) Relations
139(3)
6.2 Linear Systems with Random Inputs
142(7)
Table 6.1: Summary of Correlation and Spectral Densities
143(6)
6.3 Autoregressive Moving Average Processes (ARMA)
149(2)
6.4 Autoregressive (AR) Process
151(3)
6.5 Parametric Representations of Stochastic Processes: ARMA and ARMAX Models
154(7)
Table 6.2: Linear Systems and Random Signals
154(5)
Table 6.3: ARMAX Representation
159(1)
Table 6.4: MA Representation
160(1)
Table 6.5: AR Representation
160(1)
Hints-Suggestions-Solutions for the Exercises
161(6)
Chapter 7 Least Squares-Optimum Filtering 167(44)
7.1 Introduction
167(1)
7.2 The Least-Squares Approach
167(3)
7.3 Linear Least Squares
170(2)
7.3.1 Matrix Formulation of Linear Least Squares (LLS)
171(1)
7.4 Point Estimation
172(12)
7.4.1 Estimator Performance
173(2)
7.4.2 Biased and Unbiased Estimators
175(1)
7.4.3 Cramer-Rao Lower Bound (CRLB)
175(3)
7.4.4 Mean Square Error Criterion
178(1)
7.4.5 Maximum Likelihood Estimator
178(6)
7.5 Mean Square Error (MSE)
184(2)
7.6 Finite Impulse Response (FIR) Wiener Filter
186(4)
7.7 Wiener Solution-Orthogonal Principle
190(3)
7.7.1 Orthogonality Condition
193(1)
7.8 Wiener Filtering Examples
193(12)
7.8.1 Linear Prediction
204(1)
Hints, Suggestions, and Solutions of the Exercises
205(6)
Chapter 8 Nonparametric (Classical) Spectra Estimation 211(34)
8.1 Periodogram and Correlogram Spectra Estimation
211(11)
8.1.1 Deterministic Signals (see also
Chapter 2)
211(1)
8.1.2 The Periodogram-Random Signals
212(2)
8.1.3 Correlogram
214(1)
8.1.4 Computation of Periodogram and Correlogram Using FFT
215(9)
Windowed Periodogram
221(1)
8.2 Book Proposed Method for Better Resolution Using Transformation of the Random Variables
222(1)
8.3 Daniel Periodogram
223(1)
8.4 Bartlett Periodogram
224(5)
8.4.1 Book-Modified Method
226(3)
8.5 Blackman-Tukey (BT) Method
229(4)
8.6 Welch Method
233(6)
8.6.1 Proposed Modified Methods for Welch Method
235(28)
Modified Method Using Different Types of Overlapping
235(3)
Modified Welch Method Using RV Transformation
238(1)
Hints, Suggestions, and Solutions of the Exercises
239(2)
Appendix A8.1: Important Windows and Their Spectra
241(4)
Chapter 9 Parametric and Other Methods for Spectral Estimation 245(40)
9.1 Introduction
245(1)
9.2 AR, MA, and ARMA Models
245(2)
9.3 Yule-Walker (YW) Equations
247(4)
9.4 Least-Squares (LS) Method and Linear Prediction
251(3)
9.5 Minimum Variance Method
254(2)
9.6 Model Order
256(1)
9.7 Levinson-Durbin Algorithm
257(5)
9.8 Maximum Entropy Method
262(1)
9.9 Spectrums of Segmented Signals
263(5)
9.9.1 Method 1: The Average Method
264(1)
9.9.2 Method 2: Extrapolation Method
265(3)
9.10 Eigenvalues and Eigenvectors of Matrices (See Also Appendix 2)
268(11)
9.10.1 Eigendecomposition of the Autocorrelation Matrix
269(4)
Table 9.1: Eigenvalue Properties
270(3)
9.10.2 Harmonic Model
273(4)
9.10.3 Pisarenko Harmonic Decomposition
277(1)
9.10.4 MUSIC Algorithm
278(1)
Hints, Suggestions, and Solutions of the Exercises
279(6)
Chapter 10 Newton's and Steepest Descent Methods 285(22)
10.1 Geometric Properties of the Error Surface
285(3)
10.2 One-Dimensional Gradient Search Method
288(3)
10.2.1 Gradient Search Algorithm
289(1)
10.2.2 Newton's Method in Gradient Search
290(1)
10.3 Steepest Descent Algorithm
291(6)
10.3.1 Steepest Descent Algorithm Applied to Wiener Filter
292(2)
10.3.2 Stability (Convergence) of the Algorithm
294(1)
10.3.3 Transient Behavior of MSE
295(2)
10.3.4 Learning Curve
297(1)
10.4 Newton's Method
297(2)
10.5 Solution of the Vector Difference Equation
299(3)
Additional Exercises
302(1)
Hints, Suggestions, and Solutions of the Exercises
302(5)
Chapter 11 The Least Mean Square (LMS) Algorithm 307(26)
11.1 Introduction
307(1)
11.2 The LMS Algorithm
307(3)
Table 11.2.1: The LMS Algorithm for an Mth-Order FIR Filter
309(1)
11.3 Example Using the LMS Algorithm
310(8)
11.4 Performance Analysis of the LMS Algorithm
318(9)
11.4.1 Learning Curve
320(2)
11.4.2 The Coefficient-Error or Weighted-Error Correlation Matrix
322(2)
11.4.3 Excess MSE and Misadjustment
324(2)
11.4.4 Stability
326(1)
11.4.5 The LMS and Steepest-Descent Method
327(1)
11.5 Complex Representation of the LMS Algorithm
327(3)
Hints, Suggestions, and Solutions of the Exercises
330(3)
Chapter 12 Variants of Least Mean Square Algorithm 333(52)
12.1 The Normalized Least Mean Square Algorithm
333(4)
Table 12.1: Some Variants of the LMS Formulas
334(1)
Table 12.2: Normalized Real and Complex LMS Algorithms
334(3)
12.2 Power NLMS
337(4)
12.3 Self-Correcting LMS Filter
341(1)
12.4 The Sign-Error LMS Algorithm
342(1)
12.5 The NLMS Sign-Error Algorithm
343(1)
12.6 The Sign-Regressor LMS Algorithm
344(1)
12.7 Self-Correcting Sign-Regressor LMS Algorithm
345(1)
12.8 The Normalized Sign-Regressor LMS Algorithm
346(1)
12.9 The Sign-Sign LMS Algorithm
347(2)
12.10 The Normalized Sign-Sign LMS Algorithm
349(1)
12.11 Variable Step-Size LMS
350(2)
Table 12.3: The VSLMS Algorithm
351(1)
12.12 The Leaky LMS Algorithm
352(2)
12.13 The Linearly Constrained LMS Algorithm
354(4)
Table 12.4: Linearly Constrained LMS Algorithm
357(1)
12.14 The Least Mean Fourth Algorithm
358(1)
12.15 The Least Mean Mixed Normal (LMMN) LMS Algorithm
358(1)
12.16 Short-Length Signal of the LMS Algorithm
359(1)
12.17 The Transform Domain LMS Algorithm
360(4)
12.17.1 Convergence
363(1)
12.18 The Error Normalized Step-Size LMS Algorithm
364(4)
12.19 The Robust Variable Step-Size LMS Algorithm
368(4)
12.20 The Modified LMS Algorithm
372(1)
12.21 Momentum LMS Algorithm
373(1)
12.22 The Block LMS Algorithm
374(1)
12.23 The Complex LMS Algorithm
375(2)
Table 12.5: Complex LMS Algorithm
375(2)
12.24 The Affine LMS Algorithm
377(2)
Table 12.6: The Affine Projection Algorithm
378(1)
12.25 The Complex Affine LMS Algorithm
379(1)
Table 12.7: Complex Affine Algorithm
379(1)
Hints, Solutions, and Suggestions of the Exercises
380(5)
Chapter 13 Nonlinear Filtering 385(30)
13.1 Introduction
385(1)
13.2 Statistical Preliminaries
385(11)
13.2.1 Signal and Noise Model-Robustness
385(1)
13.2.2 Point Estimation
386(1)
13.2.3 Estimator Performance
386(2)
13.2.4 Biased and Unbiased Estimator
388(1)
13.2.5 Cramer-Rao Lower Bound
388(2)
13.2.6 Mean Square Error Criterion
390(1)
13.2.7 Maximum Likelihood Estimator
390(6)
13.3 Mean Filter
396(2)
13.4 Median Filter
398(2)
13.5 Trimmed-Type Mean Filter
400(5)
13.5.1 (r-s)-Fold Trimmed Mean Filters
400(3)
13.5.2 (r,s)-Fold Winsorized Mean Filter
403(1)
13.5.3 Alpha-Trimmed Mean Filter and Alpha-Winsorized Mean Filter
403(1)
13.5.4 Alpha-Trimmed Winsorized Mean Filter
404(1)
13.6 L-Filters
405(1)
13.7 Rank-Order Statistic Filter
406(2)
13.8 Edge-Enhancement Filters
408(1)
13.9 R-Filters
409(2)
Additional Exercises
411(1)
Problems, Solutions, Suggestions, and Hints
411(4)
Appendix 1: Suggestions and Explanations for MATLAB Use 415(12)
Appendix 2: Matrix Analysis 427(10)
Appendix 3: Mathematical Formulas 437(6)
Appendix 4: MATLAB Functions 443(4)
Bibliography 447(2)
Index 449
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.
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