Contents. 3 Vector Quantization The VQ Advantage Formulation Optimality Conditions... 48

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1 Contents Part I Prelude 1 Introduction Audio Coding Basic Idea Perceptual Irrelevance Statistical Redundancy Data Modeling Resolution Challenge Perceptual Models Global Bit Allocation Joint Channel Coding Basic Architecture Performance Assessment Part II Quantization 2 Scalar Quantization Scalar Quantization Re-Quantization Uniform Quantization Formulation Midtread and Midrise Quantizers Uniformly Distributed Signals Nonuniformly Distributed Signals Nonuniform Quantization Optimal Quantization and Lloyd-Max Algorithm Companding Vector Quantization The VQ Advantage Formulation Optimality Conditions xi

2 xii Contents 3.4 LBG Algorithm Implementation Part III Data Model 4 Linear Prediction Linear Prediction Coding Open-Loop DPCM Encoder and Decoder Quantization Noise Accumulation DPCM Quantization Error Coding Gain Optimal Prediction Optimal Predictor Levinson Durbin Algorithm Whitening Filter Spectrum Estimator Noise Shaping DPCM Open-Loop DPCM Noise-Feedback Coding Transform Coding Transform Coder Optimal Bit Allocation and Coding Gain Quantization Noise AM GM Inequality Optimal Conditions Coding Gain Optimal Bit Allocation Practical Bit Allocation Energy Compaction Optimal Transform Karhunen Loeve Transform Maximal Coding Gain Spectrum Flatness Suboptimal Transforms Discrete Fourier Transform DCT Subband Coding Subband Filtering Transform Viewed as Filter Bank DFT Filter Bank General Filter Banks... 94

3 Contents xiii 6.2 Subband Coder Reconstruction Error Decimation Effects Expansion Effects Reconstruction Error Polyphase Implementation Polyphase Representation Noble Identities Efficient Subband Coder Transform Coder Optimal Bit Allocation and Coding Gain Ideal Subband Coder Optimal Bit Allocation and Coding Gain Asymptotic Coding Gain Cosine-Modulated Filter Banks Cosine Modulation Extended DFT Bank M -DFT Bank Frequency-Shifted DFT Bank CMFB Design of NPR Filter Banks Perfect Reconstruction Design of PR Filter Banks Lattice Structure Linear Phase Free Optimization Parameters Efficient Implementation Even m Odd m Modified Discrete Cosine Transform Window Function MDCT Efficient Implementation Part IV Entropy Coding 8 Entropy and Coding Entropy Coding Entropy Entropy Model Dependency Uniquely and Instantaneously Decodable Codes Uniquely Decodable Code Instantaneous and Prefix-Free Code...153

4 xiv Contents Prefix-Free Code and Binary Tree Optimal Prefix-Free Code Shannon s Noiseless Coding Theorem Entropy as the Lower Bound Upper Bound Shannon s Noiseless Coding Theorem Huffman Coding Huffman s Algorithm Optimality Codeword Siblings Proof of Optimality Block Huffman Code Efficiency Improvement Block Encoding and Decoding Recursive Coding A Fast Decoding Algorithm Part V Audio Coding 10 Perceptual Model Sound Pressure Level Absolute Threshold of Hearing Auditory Subband Filtering Subband Filtering Auditory Filters Bark Scale Critical Bands Critical Band Level Equivalent Rectangular Bandwidth Simultaneous Masking Types of Masking Spread of Masking Global Masking Threshold Temporal Masking Perceptual Bit Allocation Masked Threshold in Subband Domain Perceptual Entropy A Simple Perceptual Model Transients Resolution Challenge Pre-Echo Artifacts Fourier Uncertainty Principle Adaptation of Resolution with Time...205

5 Contents xv 11.2 Switched-Window MDCT Relaxed PR Conditions and Window Switching Window Sequencing Double-Resolution Switched MDCT Primary and Transitional Windows Look-Ahead and Window Sequencing Implementation Window Size Compromise Temporal Noise Shaping Transient-Localized MDCT Brief Window and Pre-Echo Artifacts Window Sequencing Indication of Window Sequence to Decoder Inverse TLM Implementation Triple-Resolution Switched MDCT Transient Detection General Procedure A Practical Example Joint Channel Coding M/S Stereo Coding Joint Intensity Coding Low-Frequency Effect Channel Implementation Issues Data Structure Frame-Based Processing Time Frequency Tiling Entropy Codebook Assignment Fixed Assignment Statistics-Adaptive Assignment Bit Allocation Inter-Frame Allocation Intra-Frame Allocation Bit Stream Format Frame Header Audio Channels Error Protection Codes Auxiliary Data Implementation on Microprocessors Fitting to Low-Cost Microprocessors Fixed-Point Arithmetic...247

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