Discrete Cosine Transform (eBook)

Front Cover 1
Discrete Cosine Transform: Agorithms, Advantages Applications 4
Copyright Page 5
Table of Contents 6
PREFACE 10
ACKNOWLEDGMENTS 12
LIST OF ACRONYMS 14
NOTATION 18
CHAPTER 1. 
20 
1.1 Introduction 20
1.2 Organization of the Book 23
1.3 Appendices 24
1.4 References 25
CHAPTER 2. 
26 
2.1 Introduction 26
2.2 The Fourier Cosine Transform 26
2.3 Definitions 29
2.4 The Unitarity of DCTs 31
2.5 Scaling in Time 35
2.6 Shift in Time 36
2.7 The Difference Property 40
2.8 The Convolution Property 41
2.9 Summary 44
PROBLEMS 44
CHAPTER 3. DCT AND ITS RELATIONS TO THE KARHUNEN–LOEVE TRANSFORM 46
3.1 Introduction 46
3.2 The Karhunen-Loeve Transform 47
3.3 The DCT-I and DCT-II 51
3.4 Asymptotic Equivalence and the Generation of Discrete Unitary Transforms 57
3.5 Summary 66
PROBLEMS 66
CHAPTER 4. 
67 
4.1 Introduction 67
4.2 DCT via FFT 68
4.3 Direct Computation by Sparse Matrix Factorizations 72
4.4 Decimation-in-Time (DIT) and Decimation-in-Frequency (DIF) Algorithms 75
4.5 DCT via Other Discrete Transforms 81
4.6 Other Algorithms 84
4.7 Summary 100
PROBLEMS 101
CHAPTER 6. 
141 
6.1 Introduction 141
6.2 Variance Distribution 141
6.3 Energy Packing Efficiency (EPE) 142
6.4 Residual Correlation 147
6.5 Rate Distortion and Maximum Reducible Bits 147
6.6 Generalized Wiener Filtering 151
6.7 Summary 153
PROBLEMS 154
CHAPTER 5. 
107 
5.1 Introduction 107
5.2 Two-Dimensional DCT by Reduction to One-Dimensional DCT 109
5.3 Block Matrix Decomposed Algorithm 115
5.4 Computation via Two-Dimensional DFT 121
5.5 Two-Dimensional DCT via WHT 123
5.6 Hardware Implementation of DCT Processor 125
5.7 Summary 138
PROBLEMS 139
CHAPTER 7. 
155 
7.1 Introduction 155
7.2 Filtering 159
7.3 Decimation and Interpolation 160
7.4 LMS Filtering 163
7.5 Transmultiplexers 164
7.6 Speech Coding 165
7.7 Cepstral Analysis 181
7.8 Image Coding 182
7.9 DCT/VQ 226
7.10 Low Bit-Rate Coding 263
7.11 HDTV Image Coding 296
7.12 Block Structure/Distortion in Transform Image Coding 309
7.13 Activity Classification in Adaptive Transform Coding 315
7.14 HVS in Transform Coding 326
7.15 Data Compression 328
7.16 Classification 330
7.17 Surface Texture Analysis 331
7.18 Topographic Classification 331
7.19 Photovideotex 332
7.20 Pattern Recognition 335
7.21 Progressive Image Transmission 335
7.22 Printed Image Coding 357
7.23 Packet Video 358
7.24 BTC/Transform Coding 367
7.25 Summary 367
PROBLEMS 367
APPENDIX A.1: COMPUTER PROGRAMS FOR DCT-II AND IDCT-II, N = 8 AND 16 [FRA-3, FRA-4] 372
APPENDIX A.2: COMPUTER PROGRAMS FOR DCT-II AND IDCT-II, N = 8 AND 16 [FD-1, FRA-12] 393
APPENDIX A.3: PROGRAM FOR 2D 16x16 DCT AND IDCT 417
APPENDIX A.4: COMPUTER PROGRAM FOR GENERATING LLOYD-MAX QUANTIZER 423
APPENDIX A.5: COMPUTER PROGRAM FOR BLOCK QUANTIZATION 436
APPENDIX A.6: COMPUTER PROGRAM FOR DHT 440
APPENDIX A.7: COMPUTER PROGRAM FOR OCT VIA OHT 445
APPENDIX A.8: COMPUTER PROGRAM FOR DCT-IV 448
APPENDIX A.9: COMPUTER PROGRAM FOR DST 451
APPENDIX A.10: COMPUTER PROGRAM FOR DST-IV 454
APPENDIX A.11: COMPUTER PROGRAM FOR LOT 457
APPENDIX B.1: DCT VLSI CHIP MANUFACTURERS 462
APPENDIX B.2: IMAGE COMPRESSION BOARDS 466
APPENDIX B.3: MOTION ESTIMATION VLSI CHIP MANUFACTURERS 470
REFERENCES 473
INDEX 507