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E-raamat: Digital and Statistical Signal Processing

(Piraeus University of Applied Sciences, Greece), (Piraeus University of Applied Sciences, Athens, Greece), (Piraeus University of Applied Sciences, Athens, Greece)
  • Formaat: 576 pages
  • Ilmumisaeg: 03-Oct-2018
  • Kirjastus: CRC Press
  • Keel: eng
  • ISBN-13: 9780429017575
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Nowadays, many aspects of electrical and electronic engineering are essentially applications of DSP. This is due to the focus on processing information in the form of digital signals, using certain DSP hardware designed to execute software. Fundamental topics in digital signal processing are introduced with theory, analytical tables, and applications with simulation tools. The book provides a collection of solved problems on digital signal processing and statistical signal processing. The solutions are based directly on the math-formulas given in extensive tables throughout the book, so the reader can solve practical problems on signal processing quickly and efficiently.

FEATURES

Explains how applications of DSP can be implemented in certain programming environments designed for real time systems, ex. biomedical signal analysis and medical image processing. Pairs theory with basic concepts and supporting analytical tables. Includes an extensive collection of solved problems throughout the text. Fosters the ability to solve practical problems on signal processing without focusing on extended theory. Covers the modeling process and addresses broader fundamental issues.
Preface xiii
Authors xv
List of Acronyms
xvii
Section I Topics on Digital Signal Processing
1 Introduction
3(42)
1.1 Introduction
3(1)
1.2 Advantages of Digital Signal Processing
4(1)
1.3 Digitization Steps of Analog Signals
5(5)
1.3.1 Sampling
5(2)
1.3.2 Quantization
7(2)
1.3.3 Coding
9(1)
1.4 Sampling and Reconstruction of Sinusoidal Signals
10(7)
1.4.1 Proof of the Sampling Theorem and a Detailed Discussion
12(5)
1.5 Physical Sampling
17(3)
1.6 Sampling and Holding
20(1)
1.7 Non-Accurate Reconstruction of Analog Signals
21(1)
1.8 Solved Problems
22(23)
2 Discrete-Time Signals and Systems
45(68)
2.1 Discrete-Time Signals
45(1)
2.2 Basic Discrete-Time Signals
45(6)
2.2.1 Impulse Function
45(2)
2.2.2 Unit Step Function
47(1)
2.2.3 Ramp Function
47(1)
2.2.4 Unit Rectangular Function (Pulse Function)
48(1)
2.2.5 Exponential Function
48(2)
2.2.6 The Sinusoidal Sequence
50(1)
2.3 Even and Odd Discrete-Time Signals
51(2)
2.4 Energy and Power of a Discrete-Time Signal
53(1)
2.5 Conversion of the Independent and Dependant Variable
54(1)
2.6 Discrete-Time Systems
54(1)
2.7 Categories of Discrete-Time Systems
55(3)
2.7.1 Linear Discrete Systems
55(1)
2.7.2 Time-Invariant Discrete Systems
56(1)
2.7.3 Discrete Systems with Memory
57(1)
2.7.4 Invertible Discrete Systems
57(1)
2.7.5 Casual Discrete Systems
57(1)
2.7.6 Stable Discrete Systems
58(1)
2.8 System Connections
58(1)
2.9 Convolution
59(3)
2.10 Deconvolution
62(1)
2.11 Correlation --- Autocorrelation
63(1)
2.12 Difference Equations
64(1)
2.13 Discrete-Time Systems of Finite Impulse Response
65(1)
2.14 Solved Problems
66(47)
3 z-Transform
113(66)
3.1 Introduction
113(1)
3.2 From Laplace Transform to z-Transform
113(4)
3.2.1 Comparison of the s- and z-Planes into the Region of Convergence
116(1)
3.3 Properties of z-Transform
117(4)
3.3.1 Time Shift
117(1)
3.3.2 Linearity
118(1)
3.3.3 Time Reversal
118(1)
3.3.4 Convolution
119(1)
3.3.5 Differentiation in z-Plane
119(1)
3.3.6 Multiplication by an Exponential Sequence
120(1)
3.3.7 Conjugation of a Complex Sequence
120(1)
3.3.8 Initial and Final Value Theorem
121(1)
3.3.9 Correlation of Two Sequences
121(1)
3.4 Inverse z-Transform
121(3)
3.4.1 Method of Power Series Expansion (Division Method)
122(1)
3.4.2 Method of Partial Fraction Expansion
122(1)
3.4.3 Method of Complex Integration
123(1)
3.5 z-Transform in System Analysis
124(5)
3.5.1 Transfer Function of Discrete-Time Signal
124(1)
3.5.2 Causality of Discrete-Time Systems
124(1)
3.5.3 Stability of Discrete-Time Systems
125(1)
3.5.4 Transfer Function of Connected Systems
126(1)
3.5.5 Transfer Function of Discrete-Time Systems
127(2)
3.6 Formula Tables
129(1)
3.7 Solved Problems
130(49)
4 Structures for the Realization of Discrete-Time Systems
179(32)
4.1 Introduction
179(1)
4.2 Block Diagrams
179(2)
4.3 Realization Structures
181(7)
4.3.1 Implementation Structures of IIR Discrete Systems
183(3)
4.3.2 Implementation Structures of FIR Discrete Systems
186(2)
4.4 Signal Flow Graphs
188(2)
4.4.1 Mason's Gain Formula
189(1)
4.5 Solved Problems
190(21)
5 Frequency Domain Analysis
211(76)
5.1 Introduction
211(1)
5.2 Discrete-Time Fourier Transform (DTFT)
212(2)
5.3 Discrete Fourier Series (DFS)
214(2)
5.3.1 Periodic Convolution
215(1)
5.3.2 The Relation of the DFS Components and the DTFT over a Period
216(1)
5.4 Discrete Fourier Transform
216(5)
5.4.1 Properties of the DFT
218(1)
5.4.1.1 Linearity
218(1)
5.4.1.2 Circular Shift
218(1)
5.4.1.3 Circular Convolution
219(1)
5.4.1.4 Multiplication of Sequences
220(1)
5.4.1.5 Parseval's Theorem
220(1)
5.5 Fast Fourier Transform
221(8)
5.5.1 FFT Equations
221(7)
5.5.2 Computation of the IDFT Using FFT
228(1)
5.5.3 Fast Convolution
228(1)
5.5.3.1 Overlap and Add Method
228(1)
5.5.3.2 Overlap and Save Method
229(1)
5.6 Estimation of Fourier Transform through FFT
229(1)
5.7 Discrete Cosine Transform
229(2)
5.8 Wavelet Transform
231(5)
5.8.1 Wavelet Transform Theory
233(3)
5.9 Solved Problems
236(51)
6 Design of Digital Filters
287(96)
6.1 Introduction
287(1)
6.2 Types of Digital Filters
288(1)
6.3 Digital Filter Design Specifications
288(2)
6.4 Design of Digital IIR Filters
290(2)
6.5 Indirect Methods of IIR Filter Design
292(8)
6.5.1 The Impulse Invariant Method
292(1)
6.5.2 Step Invariant Method (or z-Transform Method with Sample and Hold)
293(2)
6.5.3 Backward Difference Method
295(1)
6.5.4 Forward Difference Method
296(1)
6.5.5 Bilinear or Tustin Method
297(2)
6.5.6 Matched Pole-Zero Method
299(1)
6.6 Direct Methods of IIR Filter Design
300(1)
6.6.1 Design of |H(e/ω)|2 Method
300(1)
6.6.2 The Method of Calculating h[ n]
301(1)
6.7 IIR Filter Frequency Transformations
301(2)
6.8 FIR Filters
303(1)
6.9 FIR Linear Phase Filters
304(3)
6.10 Stability of FIR Filters
307(1)
6.11 Design of FIR Filters
307(1)
6.12 The Moving Average Filters
307(2)
6.13 FIR Filter Design Using the Frequency Sampling Method
309(2)
6.14 FIR Filter Design Using the Window Method
311(6)
6.15 Optimal Equiripple FIR Filter Design
317(2)
6.16 Comparison of the FIR Filter Design Methods
319(1)
6.17 Solved Problems
320(63)
Section II Statistical Signal Processing
7 Statistical Models
383(22)
7.1 The Gaussian Distribution and Related Properties
383(9)
7.1.1 The Multivariate Gaussian Distribution
385(2)
7.1.2 The Central Limit Theorem
387(1)
7.1.3 The Chi-Squared RV Distribution
388(1)
7.1.4 Gamma Distribution
388(1)
7.1.5 The Non-Central Chi-Squared RV Distribution
389(1)
7.1.6 The Chi-Squared Mixed Distribution
389(1)
7.1.7 The Student's t-Distribution
390(1)
7.1.8 The Fisher-Snedecor F-Distribution
390(1)
7.1.9 The Cauchy Distribution
391(1)
7.1.10 The Beta Distribution
391(1)
7.2 Reproducing Distributions
392(1)
7.3 Fisher-Cochran Theorem
392(1)
7.4 Expected Value and Variance of Samples
393(2)
7.5 Statistical Sufficiency
395(10)
7.5.1 Statistical Sufficiency and Reduction Ratio
396(1)
7.5.2 Definition of Sufficient Condition
397(2)
7.5.3 Minimal Sufficiency
399(3)
7.5.4 Exponential Distributions Category
402(2)
7.5.5 Checking Whether a PDF Belongs to the Exponential Distribution Category
404(1)
8 Fundamental Principles of Parametric Estimation
405(50)
8.1 Estimation: Basic Components
405(1)
8.2 Estimation of Scalar Random Parameters
406(15)
8.2.1 Estimation of Mean Square Error (MSE)
407(2)
8.2.2 Estimation of Minimum Mean Absolute Error
409(2)
8.2.3 Estimation of Mean Uniform Error (MUE)
411(2)
8.2.4 Examples of Bayesian Estimation
413(8)
8.3 Estimation of Random Vector Parameters
421(1)
8.3.1 Squared Vector Error
421(1)
8.3.2 Uniform Vector Error
422(1)
8.4 Estimation of Non-Random (Constant) Parameters
422(19)
8.4.1 Scalar Estimation Criteria for Non-Random Parameters
423(3)
8.4.2 The Method of Statistical Moments for Scalar Estimators
426(3)
8.4.3 Scalar Estimators for Maximum Likelihood
429(4)
8.4.4 Cramer-Rao Bound (CRB) in the Estimation Variance
433(8)
8.5 Estimation of Multiple Non-Random (Constant) Parameters
441(11)
8.5.1 Cramer-Rao (CR) Matrix Bound in the Covariance Matrix
442(4)
8.5.2 Methods of Vector Estimation through Statistical Moments
446(1)
8.5.3 Maximum Likelihood Vector Estimation
447(5)
8.6 Handling of Nuisance Parameters
452(3)
9 Linear Estimation
455(24)
9.1 Constant MSE Minimization, Linear and Affine Estimation
455(1)
9.1.1 Optimal Constant Estimator of a Scalar RV
456(1)
9.2 Optimal Linear Estimator of a Scalar Random Variable
456(2)
9.3 Optimal Affine Estimator of a Scalar Random Variable θ
458(1)
9.3.1 Superposition Property of Linear/Affine Estimators
459(1)
9.4 Geometric Interpretation: Orthogonality Condition and Projection Theorem
459(4)
9.4.1 Reconsideration of the Minimum MSE Linear Estimation
460(2)
9.4.2 Minimum Affine MSE Estimation
462(1)
9.4.3 Optimization of the Affine Estimator for the Linear Gaussian Model
462(1)
9.5 Optimal Affine Vector Estimator
463(4)
9.5.1 Examples of Linear Estimation
464(3)
9.6 Non-Statistical Least Squares Technique (Linear Regression)
467(6)
9.7 Linear Estimation of Weighted LLS
473(4)
9.8 Optimization of LMWLS in Gaussian Models
477(2)
10 Fundamentals of Signal Detection
479(38)
10.1 The General Detection Problem
484(4)
10.1.1 Simple and Composite Hypotheses
485(1)
10.1.2 The Decision Function
486(2)
10.2 Bayes Approach to the Detection Problem
488(8)
10.2.1 Assign a Priori Probabilities
488(1)
10.2.2 Minimization of the Average Risk
488(1)
10.2.3 The Optimal Bayes Test Minimizes E[ C]
489(1)
10.2.4 Minimum Probability of the Error Test
490(1)
10.2.5 Evaluation of the Performance of Bayes Likelihood Ratio Test
490(1)
10.2.6 The Minimax Bayes Detector
491(2)
10.2.7 Typical Example
493(3)
10.3 Multiple Hypotheses Tests
496(6)
10.3.1 A Priori Probabilities
498(1)
10.3.2 Minimization of the Average Risk
498(3)
10.3.3 Disadvantages of Bayes Approach
501(1)
10.4 Frequentist Approach for Detection
502(4)
10.4.1 Case of Simple Hypotheses: θ ε {θ0,θ1}
502(4)
10.5 ROC Curves for Threshold Testing
506(11)
Appendix I Introduction to Matrix Algebra and Application to Signals and System 517(10)
Appendix II Solved Problems in Statistical Signal Processing 527(16)
Bibliography 543(2)
Index 545
Professor Anastasia Veloni is with Piraeus University of Applied Sciences, Department of Computer Systems Engineering, Athens, Greece. She has extensive teaching experience in a variety of courses on the Automatic Control area and is author/co-author of four textbooks, while her research interests lie in the areas of signal processing and automatic control.



Nikolaos I. Miridakis received his M.Sc. and Ph.D. degrees in Networking and Data Communications from the Department of Information Systems, Kingston University, U.K. in 2008 and from the Department of Informatics, University of Piraeus, Greece in 2012, respectively. Since 2007, he has been with the Department of Computer Systems Engineering, Piraeus University of Applied Sciences, Greece where he is an Adjunct Lecturer and Research Associate. Also, since 2012, he has been with the Department of Informatics, University of Piraeus, Greece where he is a Senior Research Associate. His research interests include wireless communications, and more specifically interference analysis and management in wireless communications, multicarrier communications, MIMO systems, statistical signal processing, diversity reception, fading channels, and cooperative communications.



Dr. Erysso Boukouvala holds a BSc in Physics from the Department of Physics, University of Athens, an MSc in Applied Optics with a distinction and a PhD in the field of Digital Image Restoration from the Department of Physics, University of Reading, U.K. She works at the Department of Mathematics and Physics at the Hellenic Air Force Academy as a member of the Laboratory Teaching Staff. Since 2005, she has also been employed as a Teaching Fellow at the Department of Computer Systems Engineering, at Piraeus University of Applied Sciences, Athens. She has a wide teaching and lab experience in a variety of courses such as Digital Signal Processing, Applied Optics, Optoelectronics, Lasers, and Mechanics. She has participated in research projects in U.K. Her research focuses on the development of Digital Image Restoration techniques.
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