本书包含用于分析和设计离散系统信号处理的工具，适合用做一学期的“数字信号处理”课程，读者对象为本科高年级学生或一年级研究生，也可供工程技术人员或科技人员自学使用。

本书使用了大量基于MATLAB的实例，以演示MATLAB解决信号处理问题的能力，从日常生活出发引出信号处理的问题，并给出实际应用，帮助理解信号处理概念。强调掌握概念与工具，而非数学推导，论述几个关键主题：模拟滤波器的设计、数字滤波器的结构与设计、快速傅里叶算法等。

本书是在数字信号领域的经典教材Digital Signal Processing-A Computer Based Approach，3e的基础上改编而成，内容涵盖了信号与信号处理、时域中的离散时间信号和系统、变换域中的离散时间信号、变换域中的LTI离散时间系统、连续时间信号的数字处理、数字滤波器的结构与设计等方面。本书的特点在于讲解上述内容的同时，给出了MATLAB程序验证，并有大量的高质量的习题和仿真作业。

本书可作为高等院校电子信息类专业本科生或低年级研究生的教材，尤其适用于双语教学，也可供有关技术、科研管理人员使用，或作为继续教育的参考书。

1 Signals and Signal Processing 1

1.1 Characterization and Classification of Signals 1

1.2 Typical Signal Processing Operations 3

   1.2.1 Simple Time-Domain Operations 3

   1.2.2 Filtering 4

   1.2.3 Multiplexing and Demultiplexing 6

   1.2.4 Signal Generation 6

1.3 Examples of Typical Signals 7

1.4 Typical Signal Processing Applications 11

   1.4.1 Sound Recording Applications 11

   1.4.2 Musical Sound Synthesis 19

   1.4.3 Echo Cancellation in Telephone Networks 21

1.5 Why Digital Signal Processing? 23

2 Discrete-Time Signals and Systems 27

2.1 Discrete-Time Signals 27

   2.1.1 Time-Domain Representation 28

   2.1.2 Operations on Sequences 31

   2.1.3 Classification of Sequences 37

  2.2 Typical Sequences and Sequence Representation 41

   2.2.1 Some Basic Sequences 41

   2.2.2 Sequences Generation Using MATLAB 49

   2.2.3 Representation of an Arbitrary Sequences 49

  2.3 Discrete-Time Systems 50

   2.3.1 Discrete-Time System Examples 50

   2.3.2 Classification of Discrete-Time System 56

   2.3.3 Impulse and Step Responses 59

  2.4 Time-Domain Characterization of LTI Discrete-Time Systems 60

   2.4.1 Input-Output Relationship 60

   2.4.2 Stability Condition in Terms of the Impulse Response 65

 2.4.3 Causality Condition in Terms of the Impulse Response 67

 2.4.4 Linear Constant Cofficient Difference Equation 67

2.5 Classification of LTI Discrete-Time Systems 68

 2.5.1 Classification Based on Impulse Response Length 68

 2.5.2 Classification Based on the Output Calculation Process 69

 2.5.3 Classification Based on the Impulse Response Coefficients 70

2.6 Summary 70

2.7 Problems 70

2.8 MATLAB Exercises 74

Discrete-Time Fourier Transform 76

3.1 The Continuous-Time Fourier Transform 76

 3.1.1 The Definition 76

 3.1.2 Energy Density Spectrum 79

 3.1.3 Band-limited Continuous-Time Signals 80

 3.1.4 The Frequency Response of an LTI Continuous-Time System 80

3.2 The Discrete-Time Fourier Transform 81

 3.2.1 Definition 81

 3.2.2 Basic Properties 83

 3.2.3 Symmetry Relations 84

 3.2.4 Convergence Condition 89

 3.2.5 Norm of a Discrete-Time Fourier Transform 94

3.3 Discrete-Time Fourier Transform Theorems 95

3.4 DTFT Computation Using MATLAB 100

3.5 The Unwrapped Phase Function 101

3.6 The Frequency Response of an LTI Discrete-Time System 103

  3.6.1 Definition 103

  3.6.2 Frequency-Domain Characterization of the LTI Discrete-Time System 105

  3.6.3 Frequency Responses of LTI Discrete-Time Systems 106

  3.6.4 Frequency Responses Computation Using MATLAB 107

  3.6.5 The Concept of Filtering 108

3.7 Phase and Group Delays 110

  3.7.1 Definition 111

  3.7.2 Phase and Group Delay computation Using MATLAB 113

3.8 Summary 114

3.9 Problems 115

3.10 MATLAB Exercises 121

 Digital Processing of Continuous-Time Signals 122

4.1 Introduction 122

4.2 sampling of Continuous-Time Signals 123

  4.2.1 The Sampling Process 123

  4.2.2 Effect of Sampling in the Frequency-Domain 126

  4.2.3 Recovery of the Analog Signal 135

  4.2.4 Implications of the Sampling Process 136

4.3 Sampling of Bandpass Signals 139

4.4 Analog Lowpass Filter Design 141

  4.4.1 Filter Specifications 141

  4.4.2 Butterworth Approximation 143

  4.4.3 Chebyshev Approximation 145

  4.4.4 Elliptic Approximation 148

  4.4.5 Linear-Phase Approximation 149

  4.4.6 Analog Filter Design Using MATLAB 149

  4.4.7 A Comparison of the Filter Types 156

4.5 Design of Analog Highpass Filters 157

4.6 Anti-Aliasing Filter Design 160

4.7 Reconstruction Filter Design 162

4.8 Summary 165

4.9 Problems 166

4.10 MATLAB Exercises 169

 Finite-Length Discrete Transforms 170

5.1 Orthogonal Transforms 170

5.2 The Discrete Fourier Transform 171

  5.2.1 Definition 172

  5.2.2 Matrix Relations 174

  5.2.3 DFT Computation Using MATLAB 175

 5.3 Relation Between the Fourier Transform and the DFT and Their Inverses 177

  5.3.1 Relation with Discrete-Time Fourier Transform 177

  5.3.2 Numerical Computation of the Fourier Transform Using the DFT 177

  5.3.3 Fourier Transform from DFT by Interpolation 179

  5.3.4 Sampling the Fourier Transform 180

5.4 Operations on Finite-Length Sequences 181

  5.4.1 Circular Shift of a Sequence 181

  5.4.2 Circular Convolution 183

5.5 Classifications of Finite-Length Sequences 186

 5.5.1 Classification Based on Conjugate Symmetry 187

 5.5.2 Classification Based on Geometric Symmetry 188

5.6 DFT Symmetry Relations 192

5.7 Discrete Fourier Transform Theorems 195

5.8 Fourier-Domain Filtering 200

5.9 Computation of the DFT of Real Sequences 202

 5.9.1 N-Point DFTS of Two Real Sequences Using a Single N-Point DFT 202

 5.9.2 2N-Point DFTs of a Real Sequences Using a Single N-Point DFT 203

5.10 Linear Convolution Using the DFT 204

 5.10.1 Linear Convolution of Two Finite-Length Sequences 204

 5.10.2 Linear Convolution of a Finite-Length Sequences with an Infinite-Length

      Sequence 204

5.11 Discrete Cosine Transform 208

 5.11.1 Definition 209

 5.11.2 DCT Properties 213

 5.11.3 DCT Computation Using MATLAB 214

5.12 Summary 216

5.13 Problems 216

5.16 MATLAB Exercises 226

z-Transform 227

6.1 Definition and Properties 227

6.2 Rational z-Transforms 231

6.3 Region of Convergence of a Rational z-Transform 233

6.4 The Inverse z-Transform 238

 6.4.1 General Expression 238

 6.4.2 Inverse z-Transform by Table Look-Up Method 240

 6.4.3 Inverse z-Transform by Partial-Fraction Expansion 240

 6.4.4 Partial-Fraction Expansion Using MATLAB 243

 6.4.5 Inverse z-Transform via Long Division 244

 6.4.6 Inverse z-Transform Using MATLAB 246

6.5 z-Transform Properties 246

6.6 Computation of the Convolution Sum of Finite-Length Sequences 255

 6.6.1 Linear Convolution 255

 6.6.2 Circular Convolution 256

6.7 The Transfer Function 258

  6.7.1 Definition 258

  6.7.2 Transfer Function Expression 259

  6.7.3 Frequency Response from Transfer Function 261

  6.7.4 Geometric Interpretation of Frequcney Response Computation 263

  6.7.5 Stability condition in Terms of Pole Locations 265

6.8 Summary 269

6.9 Problems 269

6.10 MATLAB Exercises 278

LTI Discrete-Time Systems in the Transform Domain 279

7.1 Transfer Function Classification Based on Magnitude Characteristics 279

  7.1.1 Digital Filters with Ideal Magnitude Responses 279

  7.1.2 Bounded Real Transfer Functions 281

  7.1.3 Allpass Transfer Function 282

7.2 Transfer Function Classification Based on Phase Characteristics 287

  7.2.1 Zero-Phase Transfer Function 287

  7.2.2 Linear-Phase Transfer Function 289

 7.2.3 Minimum-Phase and Maximum-Phase Transfer Functions 291

7.3 Types of linear-Phase Transfer Functions 294

 7.3.1 Frequency Responses for a FIR Filter with a Linear-Phase 294

 7.3.2 Zero Locations of Linear-Phase FIR Transfer Functions 301

7.4 Simple Digital Filters 304

 7.4.1 Simple FIR Digital Filters 304

 7.4.2 Simple IIR Digital Filters 306

 7.4.3 Comb Filters 310

7.5 Digital Two-Pairs 313

 7.5.1 Characterization 313

 7.5.2 Two-Pair Interconnection Schemes 314

7.6 Summary 315

7.7 Problems 316

7.8 MATLAB Exercises 326

Digital Filter Structures 328

8.1 Block Diagram Representation 328

 8.1.1 Basic Building Blocks 329

 8.1.2 Analysis of Block Diagrams 329

  8.1.3 The Delay-Free Loop Problem 330

  8.1.4 Canonic and Noncanonic Structures 331

  8.1.5 Signal Flow-Graph 331

8.2 Equivalent Structures 332

8.3 Basic FIR Digital Filter Structures 333

  8.3.1 Direct Forms 333

  8.3.2 Cascade Form 334

  8.3.3 Polyphase Realization 335

  8.3.4 Linear-Phase FIR Structures 337

  8.3.5 Tapped Delay Line 338

8.4 Basic IIR Digital Filter Structures 339

  8.4.1 Direct Forms 339

  8.4.2 Cascade Realizations 341

  8.4.3 Parallel Realizations 343

8.5 Realization of Basic Structures Using MATLAB 345

  8.5.1 Cascade Realization 345

 8.5.2 Parallel Realization 346

8.6 Allpass Filters 347

 8.6.1 Realization Based on the Multiplier Extraction Approach 348

 8.6.2 Realization Based on the Two-Pair Extraction Approach 352

8.7 Computational Complexity of Digital Filter Structures 357

8.8 Summary 358

8.9 Problems 358

8.10 MATLAB Exercises 365

IIR Digital Filter Design 366

9.1 Preliminary Considerations 366

 9.1.1 Digital Filter Specifications 366

 9.1.2 Selection of the Filter Type 369

 9.1.3 Basic Approach to IIR Digital Filter Design 369

 9.1.4 IIR Digital Filter Order Estimation 370

 9.1.5 Scaling the Digital Transfer Function 370

9.2 Bilinear Transformation Method of IIR Filter Design 371

 9.2.1 The Bilinear Transformation 371

 9.2.2 Design of Low-Order Digital Filters 373

9.3 Design of Lowpass IIR Digital Filters 374

9.4 Design of Highpass IIR Digital Filters 376

9.5 Spectral Transformations of IIR Filters 378

   9.5.1 Lowpass-to-Lowpass Transformation 379

   9.5.2 Other Transformations 381

   9.5.3 Spectral Transformation Using MATLAB 383

9.6 IIR Digital Filter Design Using MATLAB 384

9.7 Computer-Aided Design of IIR Digital Filters 387

   9.7.1 Basic Idea 387

   9.7.2 Group Delay Equalization of IIR Digital Filters 388

9.8 Summary 389

9.9 Problems 389

9.10 MATLAB Exercises 393

10 FIR Digital Filter Design 396

 10.1 Preliminary Considerations 396

     10.1.1 Basic Approaches to FIR Digital Filter Design 396

     10.1.2 Estimation of the Filter Order 397

10.2 FIR Filter Design Based onWindowed Fourier Series 400

     10.2.1 Least Integral-Squared Error Design of FIR Filters 400

     10.2.2 Impulse Responses of Ideal Filters 401

     10.2.3 Gibbs Phenomenon 403

     10.2.4 Fixed Window Functions 405

     10.2.5 Adjustable Window Functions 410

     10.2.6 Impulse Responses of FIR Filters with a Smooth Transition 413

10.3 Computer-Aided Design of Equiripple Linear-Phase FIR Filters 414

10.4 Design of Minimum-Phase FIR Filters 422

10.5 FIR Digital Filter Design Using MATLAB 424

     10.5.1 FIR Digital Filter Order Estimation Using MATLAB 424

     10.5.2 Equiripple Linear-Phase FIR Filter Design Using MATLAB 425

     10.5.3 Minimum-Phase FIR Filter Design Using MATLAB 433

     10.5.4 Window-Based FIR Filter Design Using MATLAB 436

10.6 Summary 439

10.7 Problems 439

10.8 MATLAB Exercises 446

11 DFT Algorithm Implementation 449

11.1 Computation of the Discrete Fourier Transform 449

     11.1.1 Goertzel's Algorithm 450

     11.1.2 Cooley-Tukey FFT Algorithms 452

     11.1.3 Inverse DFT Computation 462

 11.2 Fast DFT Algorithms Based on Index Mapping 463

     11.2.1 General Form of Cooley-Tukey FFT Algorithms 463

     11.2.2 Prime Factor Algorithms 467

 11.3 DFT and IDFT Computation Using MATLAB 470

 11.4 Sliding Discrete Fourier Transform 472

11.5 DFT Computation Over a Narrow Frequency Band 473

     11.5.1 ZoomFFT 473

     11.5.2 Chirp Fourier Transform 474

11.6 Summary 477

11.7 Problems 477

11.8 MATLAB Exercises 483

Bibliography 484