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Contents
Preface vii
1 Discrete-Time Signals in theTime Domain 1
1.1 Introduction 1
1.2 Getting Started 1
1.3 Background Review 2
1.4 MATLAB Commands Used 5
1.5 Generation of Sequences 5
1.6 Simple Operations on Sequences 10
1.7 Workspace Information 13
1.8 Other Types of Signals (Optional) 13
1.9 Background Reading 14
2 Discrete-Time Systems in theTime Domain 15
2.1 Introduction 15
2.2 Background Review 15
2.3 MATLAB Commands Used 17
2.4 Simulation of Discrete-Time Systems 19
2.5 Linear Time-Invariant Discrete-Time Systems 24
2.6 Background Reading 30
3 Discrete-Time Signals in the Frequency Domain 33
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ii
3.1 Introduction 33
3.2 Background Review 33
3.3 MATLAB Commands Used 37
3.4 Discrete-Time Fourier Transform 39
3.5 Discrete Fourier Transform 45
3.6 z-Transform 50
3.7 Background Reading 52
4 LTI Discrete-Time Systems in the Frequency Domain 55
4.1 Introduction 55
4.2 Background Review 55
4.3 MATLAB Commands Used 61
4.4 Transfer Function and Frequency Response 62
4.5 Types of Transfer Functions 64
4.6 Stability Test 70
4.7 Background Reading 71
5 Digital Processing of Continuous-Time Signals 73
5.1 Introduction 73
5.2 Background Review 73
5.3 MATLAB Commands Used 80
5.4 The Sampling Process in the Time Domain 81
5.5 Effect of Sampling in the Frequency Domain 83
5.6 Analog Lowpass Filters 84
5.7 A/D and D/A Conversions 86
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5.8 Background Reading 89
6 Digital Filter Structures 91
6.1 Introduction 91
6.2 Background Review 91
6.3 MATLAB Commands Used 101
6.4 Realization of FIR Transfer Functions 102
6.5 Realization of IIR Transfer Functions 103
6.6 Background Reading 107
7 Digital Filter Design 109
7.1 Introduction 109
7.2 Background Review 109
7.3 MATLAB Commands Used 116
7.4 IIR Filter Design 117
7.5 FIR Filter Design 120
7.6 Background Reading 127
8 Digital Filter Implementation 129
8.1 Introduction 129
8.2 Background Review 129
8.3 MATLAB Commands Used 134
8.4 Simulation of IIR Digital Filters 135
8.5 Simulation of FIR Digital Filters 141
8.6 Design of Tunable Digital Filters 142
8.7 Function Approximation 144
8.8 Background Reading 145
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9 Analysis of Finite
Word-Length Effects 147
9.1 Introduction 147
9.2 Background Review 147
9.3 MATLAB Commands Used 155
9.4 Generation and Quantization of Binary Numbers 156
9.5 Coefficient Quantization Effects 158
9.6 A/D Conversion Noise Analysis 161
9.7 Analysis of Arithmetic Roundoff Errors 163
9.8 Low-Sensitivity Digital Filters 166
9.9 Limit Cycles 167
9.10 Background Reading 168
10 Multirate Digital Signal Processing 171
10.1 Introduction 171
10.2 Background Review 171
10.3 MATLAB Commands Used 178
10.4 Basic Sampling Rate Alteration Devices 179
10.5 Decimator and Interpolator Design and Implementation 182
10.6 Design of Filter Banks 185
10.7 Design of Nyquist Filters 186
10.8 Background Reading 187
11 Advanced Projects 189
11.1 Introduction 189
11.2 Discrete Transforms 189
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