本书是数字信号处理的英文教材，介绍数字信号处理的基础理论和基本方法；引入应用实例并结合实验以强化工程应用能力；通过与MATLAB的信号系统分析方法相结合，详细讨论傅里叶变换与分析，快速傅里叶变换及其应用，数字滤波器的基本结构、基本理论与设计方法。全书共7章，主要内容包括：离散时间系统、z变换与傅里叶变换、离散傅里叶变换、快速傅里叶变换、数字滤波器结构、IIR数字滤波器设计、FIR数字滤波器设计等，章首给出思维导图，章后附习题和MATLAB习题，提供配套电子课件等。本书概念准确、结构合理、系统性强、特色鲜明，现代教学思想与工具的引入，使本书的使用范围更广。本书可作为高等学校和职业本科电子、通信和计算机等相关专业高年级本科生和研究生相关课程的教材，也供相关领域的科技工作者学习参考。

沈泉涌，浙江工业职业技术学院微电子技术专业副教授，维修电工一级技师，已收录SCI二区论文一篇,SCI三区论文一篇,发表其余专业论文十余篇，授权发明专利4项，实用新型专利9项。

目 录

Chapter 1 Discrete-Time Systems 1
1.1 Introduction 2
1.2 Discrete-Time Signals 3
1.3 Discrete-Time Systems 6
1.3.1 Linearity 6
1.3.2 Time Invariance 6
1.3.3 Causality 6
1.3.4 Stability 9
1.4 Difference Equations and Time-Domain
Response 10
1.5 Sampling of Continuous-Time Signals 14
1.5.1 Basic Principles 14
1.5.2 Sampling Theorem 15
1.6 Discrete-Time Signals and Systems with
MATLAB 22
1.7 Summary 23
Exercises 23
MATLAB Exercises 27
Chapter 2 The z Transform and Fourier
Transform 28
2.1 Introduction 29
2.2 Definition of the z Transform 30
2.3 Inverse z Transform 36
2.3.1 Computation Based on Residue
Theorem 37
2.3.2 Computation Based on Partial-Fraction Expansions 40
2.3.3 Computation Based on
Polynomial Division 41
2.3.4 Computation Based on Series
Expansion 43
2.4 Properties of the z Transform 43
2.4.1 Linearity 43
2.4.2 Time-Reversal 44
2.4.3 Time-Shift Theorem 44
2.4.4 Multiplication by An
Exponential 44
2.4.5 Complex Differentiation 45
2.4.6 Complex Conjugation 45
2.4.7 Real and Imaginary Sequences 46
2.4.8 Initial Value Theorem 46
2.4.9 Convolution Theorem 46
2.4.10 Product of Two Sequences 47
2.4.11 Parseval’s Theorem 48
2.4.12 Table of Basic z Transforms 48
2.5 Transfer Functions 48
2.6 Stability in the z Domain 51
2.7 Frequency Response 53
2.8 Fourier Transform 58
2.9 Properties of the Fourier Transform 61
2.9.1 Linearity 61
2.9.2 Time-Reversal 61
2.9.3 Symmetric and Antisymmetric
Sequences 62
2.9.4 Convolution Theorem 63
2.9.5 Product of Two Sequences 63
2.9.6 Parseval’s Theorem 63
2.10 Transfer Functions with MATLAB 63
2.11 Summary 65
Exercises 65
Chapter 3 Discrete Fourier Transforms 68
3.1 Introduction 69
3.2 Discrete Fourier Transform 69
3.3 Properties of the DFT 75
3.3.1 Linearity 75
3.3.2 Time-Reversal 75
3.3.3 Time-Shift Theorem 76
3.3.4 Circular Frequency-Shift Theorem (Modulation Theorem) 77
3.3.5 Circular Convolution in Time 77
3.3.6 Correlation 78
3.3.7 Real and Imaginary Sequences 78
3.3.8 Symmetric and Antisymmetric
Sequences 79
3.3.9 Parseval’s Theorem 81
3.3.10 Relationship between the
DFT and the z Transform 81
3.4 Digital Filtering Using the DFT 81
3.4.1 Linear and Circular
Convolutions 81
3.4.2 Overlap-and-Add Method 85
3.4.3 Overlap-and-Save Method 87
3.5 Other Discrete Transforms 90
3.5.1 Discrete Cosine Transform 91
3.5.2 Discrete Hartley Transform 95
3.5.3 Hadamard Transform 96
3.5.4 Other Important Transforms 97
3.6 Signal Representations 97
3.7 Discrete Transforms with MATLAB 100
3.8 Summary 101
Exercises 101
Chapter 4 The Fast Fourier
Transform 104
4.1 Relationship of the FFT to the DFT 105
4.2 Hints on Using FFTs in Practice 106
4.2.1 Sample Fast Enough and Long Enough 106
4.2.2 Manipulating the Time Data
Prior to Transformation 107
4.2.3 Enhancing FFT Results 108
4.2.4 Interpreting FFT Results 108
4.3 Derivation of the Radix-2 FFT
Algorithm 109
4.4 FFT Input/Output Data Index Bit
Reversal 115
4.5 Radix-2 FFT Butterfly Structures 116
4.6 Alternate Single-Butterfly Structures 119
4.7 Fast Fourier Transform with
MATLAB 122
4.8 Summary 123
Exercises 123
MATLAB Exercises 124
Chapter 5 Digital Filter Structures 125
5.1 Block Diagram Representation 126
5.1.1 Basic Building Blocks 127
5.1.2 Analysis of Block Diagrams 127
5.1.3 The Delay-Free Loop Problem 128
5.1.4 Canonic and Non-Canonic Structures 129
5.2 Equivalent Structures 130
5.3 Basic FIR Digital Filter Structures 131
5.3.1 Direct-Form Structures 131
5.3.2 Cascade-Form Structures 132
5.3.3 Polyphase Realization 132
5.3.4 Linear-Phase FIR Structures 134
5.3.5 Tapped Delay Line 135
5.4 Basic IIR Digital Filter Structures 136
5.4.1 Direct-Form Structures 136
5.4.2 Cascade Realizations 138
5.4.3 Parallel Realizations 141
5.5 Realization of Basic Structures Using
MATLAB 142
5.5.1 Cascade Realization 142
5.5.2 Parallel Realization 143
5.6 Allpass Filters 145
5.6.1 Realization Based on the
Multiplier Extraction Approach 145
5.6.2 Realization Based on the
Two-Pair Extraction Approach 149
5.7 IIR Tapped Cascaded Lattice Structures 154
5.7.1 Realization of an All-Pole
IIR Transfer Function 155
5.7.2 Gray-Markel Method 155
5.7.3 Realization Using MATLAB 158
5.8 FIR Cascaded Lattice Structures 159
5.8.1 Realization of a Pair of Arbitrary
FIR Transfer Functions 159
5.8.2 Realization of a Pair of
Mirror-Image FIR Transfer
Functions 163
5.8.3 Realization of a Pair of Power-Complementary FIR
Transfer Functions 163
5.8.4 Realization of a single FIR
Transfer Function 164
5.8.5 Realization Using MATLAB 164
5.9 Summary 165
Exercises 166
MATLAB Exercises 179
Chapter 6 IIR Digital Filter Design 181
6.1 Preliminary Considerations 182
6.1.1 Digital Filter Specifications 182
6.1.2 Selection of the Filter Type 185
6.1.3 Basic Approach to IIR
Digital Filter Design 186
6.1.4 IIR Digital Filter Order
Estimation 186
6.1.5 Scaling the Digital Transfer
Function 187
6.2 Bilinear Transformation Method of
IIR Filter Design 187
6.2.1 The Bilinear Transformation 187
6.2.2 Design of Low-Order Digital
Filters 190
6.3 Design of Lowpass IIR Digital Filters 193
6.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters 195
6.5 Spectral Transformation of IIR Filters 200
6.5.1 Lowpass-to-Lowpass Transformation 201
6.5.2 Other Transformations 204
6.5.3 Spectral Transformation Using MATLAB 205
6.6 IIR Digital Filter Design Using
MATLAB 207
6.7 Summary 210
Exercises 210
MATLAB Exercises 216
Chapter 7 FIR Digital Filter Design 218
7.1 Preliminary Considerations 219
7.1.1 Basic Approaches to FIR
Digital Filter Design 219
7.1.2 Estimation of the Filter Order 220
7.2 FIR Filter Design Based on
Windowed Fourier Series 223
7.2.1 Least Integral-Squared
Error Design of FIR Filters 223
7.2.2 Impulse Response Of
Ideal Filters 224
7.2.3 Gibbs Phenomenon 227
7.2.4 Fixed Window Function 230
7.2.5 Adjustable Window Functions 235
7.2.6 Impulse Responses of FIR
Filters with a Smooth Transition 238
7.3 Design of Minimum-Phase FIR Filters 240
7.4 FIR Digital Filter Design Using
MATLAB 242
7.4.1 FIR Digital Filter Order
Estimation Using MATLAB 242
7.4.2 Minimum-Phase FIR Filter
Design Using MATLAB 243
7.4.3 Window-Based FIR Filter
esign Using MATLAB 248
7.5 Summary 250
Exercises 251
MATLAB Exercises 259
Bibliography 263