Audio Coding (eBook)

Preface 
6 
Contents 
10 
Part I: 
16 
Chapter 1: 
17 
1.1 Audio Coding 18
1.2 Basic Idea 20
1.3 Perceptual Irrelevance 22
1.4 Statistical Redundancy 23
1.5 Data Modeling 23
1.6 Resolution Challenge 25
1.7 Perceptual Models 27
1.8 Global Bit Allocation 27
1.9 Joint Channel Coding 28
1.10 Basic Architecture 28
1.11 Performance Assessment 30
Part II: 
31 
Chapter 2: 
32 
2.1 Scalar Quantization 34
2.2 Re-Quantization 36
2.3 Uniform Quantization 37
2.3.1 Formulation 37
2.3.2 Midtread and Midrise Quantizers 38
2.3.3 Uniformly Distributed Signals 40
2.3.4 Nonuniformly Distributed Signals 41
2.3.4.1 Granular and Overload Error 41
2.3.4.2 Optimal SNR and Step Size 43
2.4 Nonuniform Quantization 46
2.4.1 Optimal Quantization and Lloyd-Max Algorithm 48
2.4.1.1 Uniform Quantizer as a Special Case 48
2.4.1.2 Lloyd-Max Algorithm 49
2.4.1.3 Performance Gain 50
2.4.2 Companding 52
2.4.2.1 Speech Processing 53
2.4.2.2 Audio Coding 54
Chapter 3: 
56 
3.1 The VQ Advantage 56
3.2 Formulation 59
3.3 Optimality Conditions 61
3.4 LBG Algorithm 61
3.5 Implementation 62
Part III: 
64 
Chapter 4: 
66 
4.1 Linear Prediction Coding 66
4.2 Open-Loop DPCM 68
4.2.1 Encoder and Decoder 68
4.2.2 Quantization Noise Accumulation 70
4.3 DPCM 72
4.3.1 Quantization Error 72
4.3.2 Coding Gain 73
4.4 Optimal Prediction 74
4.4.1 Optimal Predictor 74
4.4.2 Levinson–Durbin Algorithm 76
4.4.3 Whitening Filter 78
4.4.3.1 Infinite Prediction Order 78
4.4.3.2 Markov Process 79
4.4.3.3 Other Cases 80
4.4.4 Spectrum Estimator 81
4.5 Noise Shaping 82
4.5.1 DPCM 82
4.5.2 Open-Loop DPCM 84
4.5.3 Noise-Feedback Coding 84
Chapter 5: 
86 
5.1 Transform Coder 86
5.2 Optimal Bit Allocation and Coding Gain 89
5.2.1 Quantization Noise 89
5.2.2 AM–GM Inequality 90
5.2.3 Optimal Conditions 91
5.2.4 Coding Gain 92
5.2.5 Optimal Bit Allocation 93
5.2.6 Practical Bit Allocation 94
5.2.7 Energy Compaction 95
5.3 Optimal Transform 95
5.3.1 Karhunen–Loeve Transform 96
5.3.2 Maximal Coding Gain 97
5.3.3 Spectrum Flatness 98
5.4 Suboptimal Transforms 98
5.4.1 Discrete Fourier Transform 99
5.4.2 DCT 101
5.4.2.1 Type-II DCT 101
5.4.2.2 Type-IV DCT 102
Chapter 6: 
103 
6.1 Subband Filtering 103
6.1.1 Transform Viewed as Filter Bank 104
6.1.2 DFT Filter Bank 105
6.1.3 General Filter Banks 106
6.2 Subband Coder 108
6.3 Reconstruction Error 109
6.3.1 Decimation Effects 110
6.3.2 Expansion Effects 112
6.3.3 Reconstruction Error 114
6.4 Polyphase Implementation 115
6.4.1 Polyphase Representation 115
6.4.1.1 Type-I Polyphase Representation 115
6.4.1.2 Type-II Polyphase Representation 118
6.4.2 Noble Identities 119
6.4.2.1 Decimation 119
6.4.2.2 Interpolation 120
6.4.3 Efficient Subband Coder 121
6.4.4 Transform Coder 121
6.5 Optimal Bit Allocation and Coding Gain 122
6.5.1 Ideal Subband Coder 122
6.5.2 Optimal Bit Allocation and Coding Gain 123
6.5.3 Asymptotic Coding Gain 124
Chapter 7: 
126 
7.1 Cosine Modulation 126
7.1.1 Extended DFT Bank 127
7.1.2 2M-DFT Bank 128
7.1.3 Frequency-Shifted DFT Bank 130
7.1.4 CMFB 131
7.2 Design of NPR Filter Banks 133
7.3 Perfect Reconstruction 134
7.4 Design of PR Filter Banks 135
7.4.1 Lattice Structure 135
7.4.1.1 Paraunitary Systems 135
7.4.1.2 Givens Rotation 136
7.4.1.3 Delay Matrix 136
7.4.1.4 Rotation Vector 137
7.4.1.5 Cascade of Paraunitary Matrices 137
7.4.1.6 Power-Complementary Condition 138
7.4.2 Linear Phase 138
7.4.3 Free Optimization Parameters 140
7.4.3.1 Even M 140
7.4.3.2 Odd M 141
7.5 Efficient Implementation 142
7.5.1 Even m 142
7.5.2 Odd m 145
7.6 Modified Discrete Cosine Transform 147
7.6.1 Window Function 147
7.6.2 MDCT 148
7.6.3 Efficient Implementation 149
Part IV: 
153 
Chapter 8: 
154 
8.1 Entropy Coding 155
8.2 Entropy 157
8.2.1 Entropy 157
8.2.2 Model Dependency 159
8.3 Uniquely and Instantaneously Decodable Codes 161
8.3.1 Uniquely Decodable Code 161
8.3.2 Instantaneous and Prefix-Free Code 162
8.3.3 Prefix-Free Code and Binary Tree 163
8.3.4 Optimal Prefix-Free Code 164
8.4 Shannon's Noiseless Coding Theorem 165
8.4.1 Entropy as the Lower Bound 165
8.4.2 Upper Bound 167
8.4.3 Shannon's Noiseless Coding Theorem 168
Chapter 9: 
170 
9.1 Huffman's Algorithm 170
9.2 Optimality 172
9.2.1 Codeword Siblings 172
9.2.2 Proof of Optimality 174
9.3 Block Huffman Code 175
9.3.1 Efficiency Improvement 176
9.3.2 Block Encoding and Decoding 178
9.4 Recursive Coding 178
9.5 A Fast Decoding Algorithm 179
Part V: 
180 
Chapter 
181 
10.1 Sound Pressure Level 182
10.2 Absolute Threshold of Hearing 182
10.3 Auditory Subband Filtering 184
10.3.1 Subband Filtering 184
10.3.2 Auditory Filters 185
10.3.3 Bark Scale 187
10.3.4 Critical Bands 187
10.3.5 Critical Band Level 192
10.3.6 Equivalent Rectangular Bandwidth 192
10.4 Simultaneous Masking 193
10.4.1 Types of Masking 194
10.4.1.1 Tone Masking Tone 195
10.4.1.2 Tone Masking Noise 195
10.4.1.3 Noise Masking Noise 195
10.4.1.4 Noise Masking Tone 195
10.4.1.5 Practical Masking Index 196
10.4.2 Spread of Masking 196
10.4.3 Global Masking Threshold 199
10.5 Temporal Masking 201
10.6 Perceptual Bit Allocation 202
10.7 Masked Threshold in Subband Domain 203
10.8 Perceptual Entropy 203
10.9 A Simple Perceptual Model 205
Chapter 11: 
207 
11.1 Resolution Challenge 207
11.1.1 Pre-Echo Artifacts 210
11.1.2 Fourier Uncertainty Principle 212
11.1.3 Adaptation of Resolution with Time 213
11.2 Switched-Window MDCT 215
11.2.1 Relaxed PR Conditions and Window Switching 215
11.2.2 Window Sequencing 217
11.3 Double-Resolution Switched MDCT 218
11.3.1 Primary and Transitional Windows 218
11.3.2 Look-Ahead and Window Sequencing 221
11.3.3 Implementation 222
11.3.4 Window Size Compromise 223
11.4 Temporal Noise Shaping 223
11.5 Transient-Localized MDCT 225
11.5.1 Brief Window and Pre-Echo Artifacts 225
11.5.2 Window Sequencing 228
11.5.2.1 Long Windows 229
11.5.2.2 Short Windows 229
11.5.3 Indication of Window Sequence to Decoder 230
11.5.4 Inverse TLM Implementation 231
11.6 Triple-Resolution Switched MDCT 232
11.7 Transient Detection 234
11.7.1 General Procedure 235
11.7.2 A Practical Example 236
Chapter 12: 
238 
12.1 M/S Stereo Coding 238
12.2 Joint Intensity Coding 239
12.3 Low-Frequency Effect Channel 241
Chapter 13: 
242 
13.1 Data Structure 242
13.1.1 Frame-Based Processing 243
13.1.2 Time–Frequency Tiling 243
13.2 Entropy Codebook Assignment 245
13.2.1 Fixed Assignment 246
13.2.2 Statistics-Adaptive Assignment 247
13.3 Bit Allocation 248
13.3.1 Inter-Frame Allocation 248
13.3.2 Intra-Frame Allocation 249
13.4 Bit Stream Format 250
13.4.1 Frame Header 250
13.4.2 Audio Channels 251
13.4.3 Error Protection Codes 252
13.4.4 Auxiliary Data 252
13.5 Implementation on Microprocessors 253
13.5.1 Fitting to Low-Cost Microprocessors 253
13.5.2 Fixed-Point Arithmetic 254
Chapter 14: 
257 
14.1 Objective Metrics 258
14.2 Subjective Tests 258
14.2.1 Double-Blind Principle 259
14.2.2 ABX Test 259
14.2.3 ITU-R BS.1116 259
Chapter 15: 
261 
15.1 Design Considerations 261
15.2 Architecture 262
15.3 Bit Stream Format 264
15.3.1 Frame Synchronization 265
15.3.2 Frame Header 268
15.3.3 Audio Channels 270
15.3.3.1 Window Sequencing 271
15.3.3.2 Codebook Assignment 274
15.3.3.3 Quantization Indexes 276
15.3.3.4 Quantization Step Sizes 281
15.3.3.5 Sum/Difference Coding Decisions 282
15.3.3.6 Steering Vector for Joint Intensity Coding 284
15.3.4 Window Sequencing for LFE Channels 284
15.3.5 End of Frame Signature 285
15.3.6 Auxiliary Data 286
15.3.7 Unpacking the Whole Frame 286
15.4 Decoding 287
15.4.1 Inverse Quantization 287
15.4.2 Joint Intensity Decoding 288
15.4.3 Sum/Difference Decoding 289
15.4.4 De-Interleaving 291
15.4.5 Window Sequencing 292
15.4.6 Inverse TLM 295
15.4.7 Decoding the Whole Frame 295
15.5 Formal Listening Tests 296
Appendix A 
298 
A.1 Quantization Step Size 298
A.2 Critical Bands for Short and Long MDCT 299
A.3 Huffman Codebooks for Codebook Assignment 306
A.4 Huffman Codebooks for Quotient Width of Quantization Indexes 308
A.5 Huffman Codebooks for Quantization Indexes in Quasi-Stationary Frames 309
A.6 Huffman Codebooks for Quantization Indexes in Frames with Transients 323
A.7 Huffman Codebooks for Indexes of QuantizationStep Sizes 337
References 340
Index 344