Udo Zölzer is Professor of Signal Processing and Communication at Helmut Schmidt University, Hamburg, Germany. His research interests include audio and video signal processing and communications. He is the author of several books including DAFX: Digital Audio Effects.

Preface for the Third Edition viii Preface for the Second Edition ix Preface for the First Edition x 1 Introduction 1U Zölzer 1.1 Continuous-time Signals and Convolution 1 1.2 Continuous-time Fourier Transform and Laplace Transform 6 1.3 Sampling and Reconstruction 6 1.4 Discrete-time Signals and Convolution 8 1.5 Discrete-time Fourier Transform and Z-Transform 11 1.6 Discrete Fourier Transform 11 1.7 FIR and IIR Filters 12 1.8 Adaptive Filters 18 1.9 Exercises 21 References 23 2 Quantization 25U Zölzer 2.1 Signal Quantization 25 2.1.1 Classical Quantization Model 25 2.1.2 Quantization Theorem 28 2.1.3 Statistics of Quantization Error 34 2.2 Dither 40 2.2.1 Basics 40 2.2.2 Implementation 44 2.2.3 Examples 44 2.3 Spectrum Shaping of Quantization - Noise Shaping 46 2.4 Number Representation 51 2.4.1 Fixed-point Number Representation 52 2.4.2 Floating-point Number Representation 57 2.4.3 Effects on Format Conversion and Algorithms 60 2.5 JS Applet - Quantization, Dither, and Noise Shaping 62 2.6 Exercises 64 References 65 3 Sampling Rate Conversion 67U Zölzer 3.1 Basics 67 3.1.1 Upsampling and Anti-Imaging Filtering 68 3.1.2 Downsampling and Antialiasing Filtering 69 3.2 Synchronous Conversion 70 3.3 Asynchronous Conversion 74 3.3.1 Single-stage Methods 76 3.3.2 Multistage Methods 78 3.3.3 Control of Interpolation Filters 80 3.4 Interpolation Methods 83 3.4.1 Polynomial Interpolation 83 3.4.2 Lagrange Interpolation 85 3.4.3 Spline Interpolation 87 3.5 Exercises 94 References 95 4 AD/DA Conversion 97U Zölzer 4.1 Methods 97 4.1.1 Nyquist Sampling 97 4.1.2 Oversampling 98 4.1.3 Delta-sigma Modulation 100 4.2 AD Converters 113 4.2.1 Specifications 113 4.2.2 Parallel Converter 116 4.2.3 Successive Approximation 117 4.2.4 Counter Methods 118 4.2.5 Delta-sigma AD Converter 120 4.3 DA Converters 120 4.3.1 Specifications 121 4.3.2 Switched Voltage and Current Sources 123 4.3.3 Weighted Resistors and Capacitors 124 4.3.4 R-2R Resistor Networks 126 4.3.5 Delta-sigma DA Converter 127 4.4 JS Applet - Oversampling and Quantization 127 4.5 Exercises 129 References 130 5 Audio Processing Systems 131U Zölzer and D Ahlers 5.1 Digital Signal Processors 132 5.1.1 Fixed-point DSPs 132 5.1.2 Floating-point DSPs 133 5.2 Digital Audio Interfaces 133 5.2.1 Two-channel AES/EBU Interface 134 5.2.2 MADI Interface 135 5.2.3 Audio in HDMI 139 5.2.4 Audio Computer Interfaces 140 5.2.5 Audio Network Interfaces 141 5.3 Two-channel Systems 146 5.4 Multi-channel Systems 146 References 147 6 Equalizers 149U Zölzer 6.1 Basics 149 6.2 Recursive Audio Filters 153 6.2.1 Design 153 6.2.2 Parametric Filter Structures 162 6.2.3 Quantization Effects 172 6.3 Non-recursive Audio Filters 190 6.3.1 Basics of Fast Convolution 191 6.3.2 Fast Convolution of Long Sequences 194 6.3.3 Filter Design by Frequency Sampling 201 6.4 Multi-complementary Filter Bank 202 6.4.1 Principles 203 6.4.2 Example: Eight-band Multi-complementary Filter Bank 208 6.5 Delay-based Audio Effects 214 6.6 JS Applet - Audio Filters 215 6.7 Exercises 217 References 220 7 Room Simulation 225U Zölzer, P Nowak, and P Bhattacharya 7.1 Basics 225 7.1.1 Room Acoustics 225 7.1.2 Model-based Room Impulse Responses 227 7.1.3 Measurement of Room Impulse Responses 230 7.1.4 Simulation of Room Impulse Responses 234 7.2 Early Reflections 235 7.2.1 Ando's Investigations 235 7.2.2 Gerzon Algorithm 236 7.3 Subsequent Reverberation 241 7.3.1 Schroeder Algorithm 241 7.3.2 General Feedback Systems 249 7.3.3 Feedback Allpass Systems 252 7.4 Approximation of Room Impulse Responses 256 7.5 JS Applet - Fast Convolution 258 7.6 Exercises 259 References 260 8 Dynamic Range Control 265U Zölzer and E Gerat 8.1 Basics 265 8.2 Static Curve 266 8.3 Dynamic Behavior 269 8.3.1 Level Measurement 269 8.3.2 Gain Factor Smoothing 272 8.3.3 Time Constants 272 8.4 Implementation 273 8.4.1 Limiter 273 8.4.2 Compressor 274 8.4.3 Compressor, Expander, Noise Gate 276 8.4.4 Combination System 276 8.5 Realization Aspects 278 8.5.1 Sampling Rate Reduction 278 8.5.2 Curve Approximation 279 8.5.3 Stereo Processing 280 8.6 Multiband DRC 280 8.7 Dynamic Equalizers 281 8.8 Source-filter DRC 283 8.8.1 Introduction 283 8.8.2 Combination with DRC 284 8.8.3 Applications 284 8.9 JS Applet - Dynamic Range Control 287 8.10 Exercises 288 References 289 9 Audio Coding 291U Zölzer and P Bhattacharya 9.1 Lossless Audio Coding 291 9.2 Lossy Audio Coding 293 9.3 Psychoacoustics 295 9.3.1 Critical Bands and Absolute Threshold 295 9.3.2 Masking 297 9.4 ISO-MPEG1 Audio Coding 303 9.4.1 Filter Banks 303 9.4.2 Psychoacoustic Models 305 9.4.3 Dynamic Bit Allocation and Coding 309 9.5 MPEG-2 Audio Coding 310 9.6 MPEG-2 Advanced Audio Coding 310 9.7 MPEG-4 Audio Coding 321 9.8 Spectral Band Replication 325 9.9 Constrained Energy Lapped Transform - Gain and Shape Coding 327 9.9.1 Gain Quantization 329 9.9.2 Shape Quantization 330 9.9.3 Range Coding 331 9.9.4 CELT Decoding 332 9.10 JS Applet - Psychoacoustics 333 9.11 Exercises 333 References 334 10 Nonlinear Processing 341M Holters and L Köper 10.1 Fundamentals 341 10.2 Overdrive, Distortion, Clipping 343 10.3 Nonlinear Filters 347 10.4 Aliasing and its Mitigation 350 10.5 Virtual Analog Modeling 354 10.5.1 Wave Digital Filters 355 10.5.2 State-space Approaches 359 10.6 Exercises 363 References 364 11 Machine Learning for Audio 367P Bhattacharya, P Nowak, and U Zölzer 11.1 Introduction 367 11.2 Unsupervised and Supervised Learning 368 11.3 Gradient Descent and Backpropagation 369 11.3.1 Feedforward Artificial Neural Network 369 11.3.2 Convolutional Neural Network 373 11.4 Applications 375 11.4.1 Parametric Filter Adaptation 375 11.4.2 Room Simulation 383 11.4.3 Audio Denoising 388 11.5 Exercises 394 References 394 Index 401