Digital Signal Processing (eBook)

Front Cover 1
Digital Signal Processing 4
Copyright Page 5
Contents 6
Preface 14
About the Author 18
Chapter 1: Introduction to Digital Signal Processing 19
Objectives 19
1.1 Basic Concepts of Digital Signal Processing 19
1.2 Basic Digital Signal Processing Examples in Block Diagrams 21
1.2.1 Digital Filtering 21
1.2.2 Signal Frequency (Spectrum) Analysis 22
1.3 Overview of Typical Digital Signal Processing in Real-World Applications 24
1.3.1 Digital Crossover Audio System 24
1.3.2 Interference Cancellation in Electrocardiography 25
1.3.3 Speech Coding and Compression 25
1.3.4 Compact-Disc Recording System 27
1.3.5 Digital Photo Image Enhancement 28
1.4 Digital Signal Processing Applications 29
1.5 Summary 30
References 30
Chapter 2: Signal Sampling and Quantization 31
Objectives 31
2.1 Sampling of Continuous Signal 31
2.2 Signal Reconstruction 38
2.2.1 Practical Considerations for Signal Sampling: Anti-Aliasing Filtering 43
2.2.2 Practical Considerations for Signal Reconstruction: Anti-Image Filter and Equalizer 47
2.3 Analog-to-Digital Conversion, Digital-to-Analog Conversion, and Quantization 53
2.4 Summary 67
2.5 MATLAB Programs 68
2.6 Problems 69
References 74
Chapter 3: Digital Signals and Systems 75
Objectives 75
3.1 Digital Signals 75
3.1.1 Common Digital Sequences 76
3.1.2 Generation of Digital Signals 80
3.2 Linear Time-Invariant, Causal Systems 82
3.2.1 Linearity 82
3.2.2 Time Invariance 83
3.2.3 Causality 85
3.3 Difference Equations and Impulse Responses 86
3.3.1 Format of Difference Equation 86
3.3.2 System Representation Using Its Impulse Response 87
3.4 Bounded-in-and-Bounded-out Stability 90
3.5 Digital Convolution 92
3.6 Summary 100
3.7 Problems 101
Chapter 4: Discrete Fourier Transform and Signal Spectrum 105
Objectives 105
4.1 Discrete Fourier Transform 105
4.1.1 Fourier Series Coefficients of Periodic Digital Signals 106
4.1.2 Discrete Fourier Transform Formulas 110
4.2 Amplitude Spectrum and Power Spectrum 116
4.3 Spectral Estimation Using Window Functions 128
4.4 Application to Speech Spectral Estimation 138
4.5 Fast Fourier Transform 138
4.5.1 Method of Decimation-in-Frequency 140
4.5.2 Method of Decimation-in-Time 145
4.6 Summary 149
4.7 Problems 149
References 152
Chapter 5: The z-Transform 153
Objectives 153
5.1 Definition 153
5.2 Properties of the z-Transform 157
5.3 Inverse z-Transform 160
5.3.1 Partial Fraction Expansion Using MATLAB 166
5.4 Solution of Difference Equations Using the z-Transform 169
5.5 Summary 173
5.6 Problems 174
Reference 176
Chapter 6: Digital Signal Processing Systems, Basic Filtering Types, and Digital Filter Realizations 177
Objectives 177
6.1 The Difference Equation and Digital Filtering 177
6.2 Difference Equation and Transfer Function 183
6.2.1 Impulse Response, Step Response, and System Response 187
6.3 The z-Plane Pole-Zero Plot and Stability 189
6.4 Digital Filter Frequency Response 197
6.5 Basic Types of Filtering 206
6.6 Realization of Digital Filters 213
6.6.1 Direct-Form I Realization 213
6.6.2 Direct-Form II Realization 214
6.6.3 Cascade (Series) Realization 215
6.6.4 Parallel Realization 216
6.7 Application: Speech Enhancement and Filtering 220
6.7.1 Pre-Emphasis of Speech 220
6.7.2 Bandpass Filtering of Speech 223
6.8 Summary 226
6.9 Problems 227
Reference 232
Chapter 7: Finite Impulse Response Filter Design 233
Objectives 233
7.1 Finite Impulse Response Filter Format 233
7.2 Fourier Transform Design 235
7.3 Window Method 247
7.4 Applications: Noise Reduction and Two-Band Digital Crossover 271
7.4.1 Noise Reduction 271
7.4.2 Speech Noise Reduction 273
7.4.3 Two-Band Digital Crossover 274
7.5 Frequency Sampling Design Method 278
7.6 Optimal Design Method 286
7.7 Realization Structures of Finite Impulse Response Filters 298
7.7.1 Transversal Form 298
7.7.2 Linear Phase Form 300
7.8 Coefficient Accuracy Effects on Finite Impulse Response Filters 301
7.9 Summary of Finite Impulse Response (FIR) Design Procedures and Selection of FIR Filter Design Methods in Practice 305
7.10 Summary 308
7.11 MATLAB Programs 309
7.12 Problems 312
References 319
Chapter 8: Infinite Impulse Response Filter Design 321
Objectives 321
8.1 Infinite Impulse Response Filter Format 321
8.2 Bilinear Transformation Design Method 323
8.2.1 Analog Filters Using Lowpass Prototype Transformation 324
8.2.2 Bilinear Transformation and Frequency Warping 328
8.2.3 Bilinear Transformation Design Procedure 335
8.3 Digital Butterworth and Chebyshev Filter Designs 340
8.3.1 Lowpass Prototype Function and Its Order 340
8.3.2 Lowpass and Highpass Filter Design Examples 344
8.3.3 Bandpass and Bandstop Filter Design Examples 354
8.4 Higher-Order Infinite Impulse Response Filter Design Using the Cascade Method 361
8.5 Application: Digital Audio Equalizer 364
8.6 Impulse Invariant Design Method 368
8.7 Polo-Zero Placement Method for Simple Infinite Impulse Response Filters 376
8.7.1 Second-Order Bandpass Filter Design 377
8.7.2 Second-Order Bandstop (Notch) Filter Design 378
8.7.3 First-Order Lowpass Filter Design 380
8.7.4 First-Order Highpass Filter Design 382
8.8 Realization Structures of Infinite Impulse Response Filters 383
8.8.1 Realization of Infinite Impulse Response Filters in Direct-Form I and Direct-Form II 384
8.8.2 Realization of Higher-Order Infinite Impulse Response Filters via the Cascade Form 386
8.9 Application: 60-Hz Hum Eliminator and Heart Rate Detection Using Electrocardiography 388
8.10 Coefficient Accuracy Effects on Infinite Impulse Response Filters 395
8.11 Application: Generation and Detection of Dual-Tone Multifrequency Tones Using Goertzel Algorithm 399
8.11.1 Single-Tone Generator 400
8.11.2 Dual-Tone Multifrequency Tone Generator 402
8.11.3 Goertzel Algorithm 404
8.11.4 Dual-Tone Multifrequency Tone Detection Using the Modified Goertzel Algorithm 409
8.12 Summary of Infinite Impulse Response (IIR) Design Procedures and Selection of the IIR Filter Design Methods in Practice 414
8.13 Summary 419
8.14 Problems 420
References 430
Chapter 9: Hardware and Software for Digital Signal Processors 431
Objectives 431
9.1 Digital Signal Processor Architecture 431
9.2 Digital Signal Processor Hardware Units 434
9.2.1 Multiplier and Accumulator 434
9.2.2 Shifters 435
9.2.3 Address Generators 436
9.3 Digital Signal Processors and Manufactures 437
9.4 Fixed-Point and Floating-Point Formats 438
9.4.1 Fixed-Point Format 438
9.4.2 Floating-Point Format 447
9.4.3 IEEE Floating-Point Formats 452
9.4.5 Fixed-Point Digital Signal Processors 455
9.4.6 Floating-Point Processors 457
9.5 Finite Impulse Response and Infinite Impulse Response Filter Implementation in Fixed-Point Systems 459
9.6 Digital Signal Processing Programming Examples 465
9.6.1 Overview of TMS320C67x DSK 465
9.6.2 Concept of Real-Time Processing 469
9.6.3 Linear Buffering 470
9.6.4 Sample C Programs 473
9.7 Summary 478
9.8 Problems 479
References 480
Chapter 10: Adaptive Filters and Applications 481
Objectives 481
10.1 Introduction to Least Mean Square Adaptive Finite Impulse Response Filters 481
10.2 Basic Wiener Filter Theory and Least Mean Square Algorithm 485
10.3 Applications: Noise Cancellation, System Modeling, and Line Enhancement 491
10.3.1 Noise Cancellation 491
10.3.2 System Modeling 497
10.3.3 Line Enhancement Using Linear Prediction 502
10.4 Other Application Examples 504
10.4.1 Canceling Periodic Interferences Using Linear Prediction 505
10.4.2 Electrocardiography Interference Cancellation 506
10.4.3 Echo Cancellation in Long-Distance Telephone Circuits 507
10.5 Summary 509
10.6 Problems 509
References 514
Chapter 11: Waveform Quantization and Compression 515
Objectives 515
11.1 Linear Midtread Quantization 515
11.2 mu-law Companding 519
11.2.1 Analog mu-Law Companding 519
11.2.2 Digital mu-Law Companding 524
11.3 Examples of Differential Pulse Code Modulation (DPCM), Delta Modulation, and Adaptive DPCM G.721 528
11.3.1 Examples of Differential Pulse Code Modulation and Delta Modulation 528
11.3.2 Adaptive Differential Pulse Code Modulation G.721 533
11.4 Discrete Cosine Transform, Modified Discrete Cosine Transform, and Transform Coding in MPEG Audio 540
11.4.1 Discrete Cosine Transform 540
11.4.2 Modified Discrete Cosine Transform 543
11.4.3 Transform Coding in MPEG Audio 548
11.5 Summary 551
11.6 MATLAB Programs 552
11.7 Problems 568
References 573
Chapter 12: Multirate Digital Signal Processing, Oversampling of Analog-to-Digital Conversion, and Undersampling of Bandpass Signals 575
Objectives 575
12.1 Multirate Digital Signal Processing Basics 575
12.1.1 Sampling Rate Reduction by an Integer Factor 576
12.1.2 Sampling Rate Increase by an Integer Factor 582
12.1.3 Changing Sampling Rate by a Non-Integer Factor L/M 588
12.1.4 Application: CD Audio Player 593
12.1.5 Multistage Decimation 596
12.2 Polyphase Filter Structure and Implementation 601
12.3 Oversampling of Analog-to-Digital Conversion 607
12.3.1 Oversampling and Analog-to-Digital Conversion Resolution 608
12.3.2 Sigma-DeltaModulation Analog-to-Digital Conversion 611
12.4 Application Example: CD Player 617
12.5 Undersampling of Bandpass Signals 619
12.6 Summary 627
12.7 Problems 628
References 632
Chapter 13: Image Processing Basics 635
13.1 Image Processing Notation and Data Formats 635
13.1.1 8-Bit Gray Level Images 636
13.1.2 24-Bit Color Images 637
13.1.3 8-Bit Color Images 638
13.1.4 Intensity Images 639
13.1.5 Red, Green, Blue Components and Grayscale Conversion 640
13.1.6 MATLAB Functions for Format Conversion 642
13.2 Image Histogram and Equalization 643
13.2.1 Grayscale Histogram and Equalization 643
13.2.2 24-Bit Color Image Equalization 650
13.2.3 8-Bit Indexed Color Image Equalization 651
13.2.4 MATLAB Functions for Equalization 654
13.3 Image Level Adjustment and Contrast 655
13.3.1 Linear Level Adjustment 656
13.3.2 Adjusting the Level for Display 659
13.3.3 Matlab Functions for Image Level Adjustment 660
13.4 Image Filtering Enhancement 660
13.4.1 Lowpass Noise Filtering 661
13.4.2 Median Filtering 664
13.4.3 Edge Detection 669
13.4.4 MATLAB Functions for Image Filtering 673
13.5 Image Pseudo-Color Generation and Detection 675
13.6 Image Spectra 679
13.7 Image Compression by Discrete Cosine Transform 682
13.7.1 Two-Dimensional Discrete Cosine Transform 684
13.7.2 Two-Dimensional JPEG Grayscale Image Compression Example 687
13.7.3 JPEG Color Image Compression 689
13.8 Creating a Video Sequence by Mixing Two Images 695
13.9 Video Signal Basics 695
13.9.1 Analog Video 696
13.9.2 Digital Video 703
13.10 Motion Estimation in Video 705
13.11 Summary 708
13.12 Problems 710
References 716
Appendix A: Introduction to the MATLAB Environment 717
A.1 Basic Commands and Syntax 717
A.2 MATLAB Array and Indexing 721
A.3 Plot Utilities: Subplot, Plot, Stem, and Stair 722
A.4 MATLAB Script Files 722
A.5 MATLAB Functions 723
References 725
Appendix B: Review of Analog Signal Processing 727
B.1 Fourier Series and Fourier Transform 727
B.1.1 Sine-Cosine Form 727
B.1.2 Amplitude-Phase Form 728
B.1.3 Complex Exponential Form 729
B.1.4 Spectral Plots 732
B.1.5 Fourier Transform 739
B.2 Laplace Transform 744
B.2.1 Laplace Transform and Its Table 744
B.2.2 Solving Differential Equations Using Laplace Transform 745
B.2.3 Transfer Function 748
B.3 Poles, Zeros, Stability, Convolution, and Sinusoidal Steady-State Response 749
B.3.1 Poles, Zeros, and Stability 749
B.3.2 Convolution 751
B.3.3 Sinusoidal Steady-State Response 753
B.4 Problems 754
References 758
Appendix C: Normalized Butterworth and Chebyshev Fucntions 759
C.1 Normalized Butterworth Function 759
C.2 Normalized Chebyshev Function 762
Appendix D: Sinusoidal Steady-State Response of Digital Filters 767
D.1 Sinusoidal Steady-State Response 767
D.2 Properties of the Sinusoidal Steady-State Response 769
Appendix E: Finite Impulse Response Filter Design Equations by the Frequency Sampling Design Method 771
Appendix F: Some Useful Mathematical Formulas 775
Bibliography 779
Answers to Selected Problems 783
Index 809
Color Plates 835