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Oct 16, 2017

EBOOK - Digital Signal Processing - Signals Systems and Filters (Andreas Antoniou)


EBOOK - Xử lý tín hiệu số - Hệ thống và Bộ lọc tín hiệu (Andreas Antoniou) - 991 Trang.

The great advancements in the design of microchips, digital systems, and computer hardware over the past 40 years have given birth to digital signal processing(DSP) which has grown over the years into a ubiquitous, multifaceted, and indispensable subject of study. As such DSP has been applied in most disciplines ranging from engineering to economics and from astronomy to molecular biology. Consequently, it would take a multivolume encyclopedia to cover all the facets, aspects, and ramifications of DSP, and such a treatise would require many authors.
This textbook focuses instead on the fundamentals of DSP, namely, on the epresentation of signals by mathematical models and on the processing of signals by discrete-time systems. Various types of processing are possible for signals but the processing of interest in this volume is almost always linear and it typically involves reshaping, transforming, or manipulating the frequency spectrum of the signal of interest. Discretetime systems that can reshape, transform, or manipulate the spectrum of a signal are known asdigital filters, and these systems will receive very special attention as they did in the author’s previous textbookDigital Filters: Analysis, Design, and Applications, McGraw-Hill, 1993.


Chapter 1. Introduction to Digital Signal Processing 1
1.1 Introduction 1
1.2 Signals 1
1.3 Frequency-Domain Representation 4
1.4 Notation 7
1.5 Signal Processing 8
1.6 Analog Filters 15
1.7 Applications of Analog Filters 16
1.8 Digital Filters 19
1.9 Two DSP Applications 23
1.9.1 Processing of EKG signals 23
1.9.2 Processing of Stock-Exchange Data 24
References 26
Chapter 2. The Fourier Series and Fourier Transform 29
2.1 Introduction 29
2.2 Fourier Series 29
2.2.1 Definition 30
2.2.2 Particular Forms 31
2.2.3 Theorems and Properties 35
2.3 Fourier Transform 46
2.3.1 Derivation 47
2.3.2 Particular Forms 50
2.3.3 Theorems and Properties 57
References 73
Problems 73
Chapter 3. ThezTransform 79
3.1 Introduction 79
3.2 Definition ofzTransform 80
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x DIGITAL SIGNAL PROCESSING
3.3 Convergence Properties 81
3.4 ThezTransform as a Laurent Series 83
3.5 InversezTransform 85
3.6 Theorems and Properties 86
3.7 Elementary Discrete-Time Signals 95
3.8 z-Transform Inversion Techniques 101
3.8.1 Use of Binomial Series 103
3.8.2 Use of Convolution Theorem 108
3.8.3 Use of Long Division 110
3.8.4 Use of Initial-Value Theorem 113
3.8.5 Use of Partial Fractions 115
3.9 Spectral Representation of Discrete-Time Signals 119
3.9.1 Frequency Spectrum 119
3.9.2 Periodicity of Frequency Spectrum 120
3.9.3 Interrelations 124
References 126
Problems 126
Chapter 4. Discrete-Time Systems 131
4.1 Introduction 131
4.2 Basic System Properties 132
4.2.1 Linearity 132
4.2.2 Time Invariance 134
4.2.3 Causality 136
4.3 Characterization of Discrete-Time Systems 140
4.3.1 Nonrecursive Systems 140
4.3.2 Recursive Systems 140
4.4 Discrete-Time System Networks 142
4.4.1 Network Analysis 143
4.4.2 Implementation of Discrete-Time Systems 146
4.4.3 Signal Flow-Graph Analysis 147
4.5 Introduction to Time-Domain Analysis 155
4.6 Convolution Summation 163
4.6.1 Graphical Interpretation 166
4.6.2 Alternative Classification 169
4.7 Stability 171
4.8 State-Space Representation 174
4.8.1 Computability 175
4.8.2 Characterization 176
4.8.3 Time-Domain Analysis 184
4.8.4 Applications of State-Space Method 186
References 186
Problems 186
Chapter 5. The Application of thezTransform 201
5.1 Introduction 201
5.2 The Discrete-Time Transfer Function 202
5.2.1 Derivation ofH(z) from Difference Equation 202
5.2.2 Derivation ofH(z) from System Network 204
5.2.3 Derivation ofH(z) from State-Space Characterization 205
TABLE OF CONTENTS xi
5.3 Stability 207
5.3.1 Constraint on Poles 207
5.3.2 Constraint on Eigenvalues 211
5.3.3 Stability Criteria 214
5.3.4 Test for Common Factors 215
5.3.5 Schur-Cohn Stability Criterion 216
5.3.6 Schur-Cohn-Fujiwara Stability Criterion 217
5.3.7 Jury-Marden Stability Criterion 219
5.3.8 Lyapunov Stability Criterion 222
5.4 Time-Domain Analysis 223
5.5 Frequency-Domain Analysis 224
5.5.1 Steady-State Sinusoidal Response 224
5.5.2 Evaluation of Frequency Response 227
5.5.3 Periodicity of Frequency Response 228
5.5.4 Aliasing 229
5.5.5 Frequency Response of Digital Filters 232
5.6 Transfer Functions for Digital Filters 245
5.6.1 First-Order Transfer Functions 246
5.6.2 Second-Order Transfer Functions 246
5.6.3 Higher-Order Transfer Functions 251
5.7 Amplitude and Delay Distortion 251
References 254
Problems 254
Chapter 6. The Sampling Process 261
6.1 Introduction 261
6.2 Fourier Transform Revisited 263
6.2.1 Impulse Functions 263
6.2.2 Periodic Signals 272
6.2.3 Unit-Step Function 274
6.2.4 Generalized Functions 274
6.3 Interrelation Between the Fourier Series and the Fourier Transform 278
6.4 Poisson’s Summation Formula 284
6.5 Impulse-Modulated Signals 286
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