1 Signals and Signal Processing
1.1 Characterization and Classification of Signals 1
1.2 Typical Signal Processing Operations 3
1.3 Examples of Typical Signals 12
1.4 Typical Signal Processing Applications 21
1.5 Why Digital Signal Processing? 36
2 Discrete-Time Signals and Systems
2.1 Discrete-Time Signals 42
2.2 Typical Sequences and Sequence Representation 56
2.3 The Sampling Process 64
2.4 Discrete-Time Systems 67
2.5 Time-Domain Characterization of LTI Discrete-Time Systems 78
2.6 Simple Interconnection Schemes 87
2.7 Finite-Dimensional LTI Discrete-Time Systems 90
2.8 Classification of LTI Discrete-Time Systems 100
2.9 Correlation of Signals 102
2.10 Random Signals 106
2.11 Summary 107
2.12 Problems 107
2.13 Matlab Exercises 115
3 Discrete-Time Fourier Transform
3.1 The Continuous-Time Fourier Transform 117
3.2 The Discrete-Time Fourier Transform 122
3.3 Discrete-Time Fourier Transform Theorems 136
3.4 Energy Density Spectrum of a Discrete-Time Sequence 141
3.5 Band-Limited Discrete-Time Signals 143
3.6 DTFT Computation Using Matlab 143
3.7 The Unwrapped Phase Function 145
3.8 The Frequency Response of an LTI Discrete-Time System 146
3.9 Phase and Group Delays 156
3.10 Summary 160
3.11 Problems 160
3.12 Matlab Exercises 170
4 Digital Processing of Continuous-Time Signals
4.1 Introduction 171
4.2 Sampling of Continuous-Time Signals 172
4.3 Sampling of Bandpass Signals 184
4.4 Analog Lowpass Filter Design 187
4.5 Design of Analog Highpass, Bandpass, and Bandstop Filters 202
4.6 Anti-Aliasing Filter Design 209
4.7 Sample-and-Hold Circuit 211
4.8 Analog-to-Digital Converter 212
4.9 Digital-to-Analog Converter 217
4.10 Reconstruction Filter Design 221
4.11 Effect of Sample-and-Hold Operation 224
4.12 Summary 226
4.13 Problems 226
4.14 Matlab Exercises 231
5 Finite-Length Discrete Transforms
5.1 Orthogonal Transforms 233
5.2 The Discrete Fourier Transform 234
5.3 Relation Between the Fourier Transform and the DFT, and Their Inverses 240
5.4 Operations on Finite-Length Sequences 244
5.5 Classifications of Finite-Length Sequences 251
5.6 DFT Symmetry Relations 256
5.7 Discrete Fourier Transform Theorems 259
5.8 Fourier-Domain Filtering 264
5.9 Computation of the DFT of Real Sequences 266
5.10 Linear Convolution using the DFT 268
5.11 Discrete Cosine Transform 274
5.12 The Haar Transform 283
5.13 Energy Compaction Properties 286
5.14 Summary 288
5.15 Problems 289
5.16 Matlab Exercises 298
6 z-Transform
6.1 Definition and Properties 301
6.2 Rational z-Transforms 305
6.3 Region of Convergence of a Rational z-Transform 307
6.4 The Inverse z-Transform 312
6.5 z-Transform Properties 320
6.6 Computation of the Convolution Sum of Finite-Length Sequences 329
6.7 The Transfer Function 332
6.8 Summary 343
6.9 Problems 343
6.10 Matlab Exercises 351
7 LTI Discrete-Time Systems in the Transform Domain
7.1 Transfer Function Classification Based on Magnitude Characteristics 353
7.2 Transfer Function Classification Based on Phase Characteristics 361
7.3 Types of linear-Phase Transfer Functions 368
7.4 Simple Digital Filters 378
7.5 Complementary Transfer Functions 391
7.6 Inverse Systems 396
7.7 System Identification 401
7.8 Digital Two-Pairs 403
7.9 Algebraic Stability Test 406
7.10 Summary 411
7.11 Problems 411
7.12 Matlab Exercises 424
8 Digital Filter Structures
8.1 Block Diagram Representation 427
8.2 Equivalent Structures 430
8.3 Basic FIR Digital Filter Structures 432
8.4 Basic IIR Digital Filter Structures 437
8.5 Realization of Basic Structures Using Matlab 443
8.6 Allpass Filters 445
8.7 Tunable IIR Digital Filters 454
8.8 IIR Tapped Cascaded Lattice Structures 456
8.9 FIR Cascaded Lattice Structures 461
8.10 Parallel Allpass Realization of IIR Transfer Functions 467
8.11 Digital Sine-Cosine Generator 473
8.12 Computational Complexity of Digital Filter Structures 475
8.13 Summary 477
8.14 Problems 477
8.15 Matlab Exercises 487
9 IIR Digital Filter Design
9.1 Preliminary Considerations 489
9.2 Bilinear Transformation Method of IIR Filter Design 494
9.3 Design of Lowpass IIR Digital Filters 499
9.4 Design of Highpass, Bandpass, and Bandstop IIR Digital Filters 500
9.5 Spectral Transformations of IIR Filters 505
9.6 IIR Digital Filter Design Using Matlab 511
9.7 Computer-Aided Design of IIR Digital Filters 514
9.8 Summary 516
9.9 Problems 516
9.10 Matlab Exercises 521
10 FIR Digital Filter Design
10.1 Preliminary Considerations 523
10.2 FIR Filter Design Based onWindowed Fourier Series 527
10.3 Computer-Aided Design of Equiripple Linear-Phase FIR Filters 541
10.4 Design of Minimum-Phase FIR Filters 549
10.5 FIR Digital Filter Design Using Matlab 551
10.6 Design of Computationally Efficient FIR Digital Filters 566
10.7 Summary 576
10.8 Problems 578
10.9 Matlab Exercises 584
11 DSP Algorithm Implementation
11.1 Basic Issues 589
11.2 Structure Simulation and Verification Using Matlab 600
11.3 Computation of the Discrete Fourier Transform 607
11.4 Fast DFT Algorithms Based on Index Mapping 621
11.5 DFT and IDFT Computation Using Matlab 628
11.6 Sliding Discrete Fourier Transform 630
11.7 DFT Computation Over a Narrow Frequency Band 630
11.8 Number Representation 635
11.9 Arithmetic Operations 639
11.10 Handling of Overflow 644
11.11 Tunable Digital Filters 645
11.12 Function Approximation 651
11.13 Summary 654
11.14 Problems 654
11.15 Matlab Exercises 663
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