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 viiiPreface for the Second Edition ixPreface for the First Edition x1 Introduction 1U Zölzer1.1 Continuous-time Signals and Convolution 11.2 Continuous-time Fourier Transform and Laplace Transform 61.3 Sampling and Reconstruction 61.4 Discrete-time Signals and Convolution 81.5 Discrete-time Fourier Transform and Z-Transform 111.6 Discrete Fourier Transform 111.7 FIR and IIR Filters 121.8 Adaptive Filters 181.9 Exercises 21References 232 Quantization 25U Zölzer2.1 Signal Quantization 252.1.1 Classical Quantization Model 252.1.2 Quantization Theorem 282.1.3 Statistics of Quantization Error 342.2 Dither 402.2.1 Basics 402.2.2 Implementation 442.2.3 Examples 442.3 Spectrum Shaping of Quantization – Noise Shaping 462.4 Number Representation 512.4.1 Fixed-point Number Representation 522.4.2 Floating-point Number Representation 572.4.3 Effects on Format Conversion and Algorithms 602.5 JS Applet – Quantization, Dither, and Noise Shaping 622.6 Exercises 64References 653 Sampling Rate Conversion 67U Zölzer3.1 Basics 673.1.1 Upsampling and Anti-Imaging Filtering 683.1.2 Downsampling and Antialiasing Filtering 693.2 Synchronous Conversion 703.3 Asynchronous Conversion 743.3.1 Single-stage Methods 763.3.2 Multistage Methods 783.3.3 Control of Interpolation Filters 803.4 Interpolation Methods 833.4.1 Polynomial Interpolation 833.4.2 Lagrange Interpolation 853.4.3 Spline Interpolation 873.5 Exercises 94References 954 AD/DA Conversion 97U Zölzer4.1 Methods 974.1.1 Nyquist Sampling 974.1.2 Oversampling 984.1.3 Delta-sigma Modulation 1004.2 AD Converters 1134.2.1 Specifications 1134.2.2 Parallel Converter 1164.2.3 Successive Approximation 1174.2.4 Counter Methods 1184.2.5 Delta-sigma AD Converter 1204.3 DA Converters 1204.3.1 Specifications 1214.3.2 Switched Voltage and Current Sources 1234.3.3 Weighted Resistors and Capacitors 1244.3.4 R–2R Resistor Networks 1264.3.5 Delta-sigma DA Converter 1274.4 JS Applet – Oversampling and Quantization 1274.5 Exercises 129References 1305 Audio Processing Systems 131U Zölzer and D Ahlers5.1 Digital Signal Processors 1325.1.1 Fixed-point DSPs 1325.1.2 Floating-point DSPs 1335.2 Digital Audio Interfaces 1335.2.1 Two-channel AES/EBU Interface 1345.2.2 MADI Interface 1355.2.3 Audio in HDMI 1395.2.4 Audio Computer Interfaces 1405.2.5 Audio Network Interfaces 1415.3 Two-channel Systems 1465.4 Multi-channel Systems 146References 1476 Equalizers 149U Zölzer6.1 Basics 1496.2 Recursive Audio Filters 1536.2.1 Design 1536.2.2 Parametric Filter Structures 1626.2.3 Quantization Effects 1726.3 Non-recursive Audio Filters 1906.3.1 Basics of Fast Convolution 1916.3.2 Fast Convolution of Long Sequences 1946.3.3 Filter Design by Frequency Sampling 2016.4 Multi-complementary Filter Bank 2026.4.1 Principles 2036.4.2 Example: Eight-band Multi-complementary Filter Bank 2086.5 Delay-based Audio Effects 2146.6 JS Applet – Audio Filters 2156.7 Exercises 217References 2207 Room Simulation 225U Zölzer, P Nowak, and P Bhattacharya7.1 Basics 2257.1.1 Room Acoustics 2257.1.2 Model-based Room Impulse Responses 2277.1.3 Measurement of Room Impulse Responses 2307.1.4 Simulation of Room Impulse Responses 2347.2 Early Reflections 2357.2.1 Ando’s Investigations 2357.2.2 Gerzon Algorithm 2367.3 Subsequent Reverberation 2417.3.1 Schroeder Algorithm 2417.3.2 General Feedback Systems 2497.3.3 Feedback Allpass Systems 2527.4 Approximation of Room Impulse Responses 2567.5 JS Applet – Fast Convolution 2587.6 Exercises 259References 2608 Dynamic Range Control 265U Zölzer and E Gerat8.1 Basics 2658.2 Static Curve 2668.3 Dynamic Behavior 2698.3.1 Level Measurement 2698.3.2 Gain Factor Smoothing 2728.3.3 Time Constants 2728.4 Implementation 2738.4.1 Limiter 2738.4.2 Compressor 2748.4.3 Compressor, Expander, Noise Gate 2768.4.4 Combination System 2768.5 Realization Aspects 2788.5.1 Sampling Rate Reduction 2788.5.2 Curve Approximation 2798.5.3 Stereo Processing 2808.6 Multiband DRC 2808.7 Dynamic Equalizers 2818.8 Source-filter DRC 2838.8.1 Introduction 2838.8.2 Combination with DRC 2848.8.3 Applications 2848.9 JS Applet – Dynamic Range Control 2878.10 Exercises 288References 2899 Audio Coding 291U Zölzer and P Bhattacharya9.1 Lossless Audio Coding 2919.2 Lossy Audio Coding 2939.3 Psychoacoustics 2959.3.1 Critical Bands and Absolute Threshold 2959.3.2 Masking 2979.4 ISO-MPEG1 Audio Coding 3039.4.1 Filter Banks 3039.4.2 Psychoacoustic Models 3059.4.3 Dynamic Bit Allocation and Coding 3099.5 MPEG-2 Audio Coding 3109.6 MPEG-2 Advanced Audio Coding 3109.7 MPEG-4 Audio Coding 3219.8 Spectral Band Replication 3259.9 Constrained Energy Lapped Transform – Gain and Shape Coding 3279.9.1 Gain Quantization 3299.9.2 Shape Quantization 3309.9.3 Range Coding 3319.9.4 CELT Decoding 3329.10 JS Applet – Psychoacoustics 3339.11 Exercises 333References 33410 Nonlinear Processing 341M Holters and L Köper10.1 Fundamentals 34110.2 Overdrive, Distortion, Clipping 34310.3 Nonlinear Filters 34710.4 Aliasing and its Mitigation 35010.5 Virtual Analog Modeling 35410.5.1 Wave Digital Filters 35510.5.2 State-space Approaches 35910.6 Exercises 363References 36411 Machine Learning for Audio 367P Bhattacharya, P Nowak, and U Zölzer11.1 Introduction 36711.2 Unsupervised and Supervised Learning 36811.3 Gradient Descent and Backpropagation 36911.3.1 Feedforward Artificial Neural Network 36911.3.2 Convolutional Neural Network 37311.4 Applications 37511.4.1 Parametric Filter Adaptation 37511.4.2 Room Simulation 38311.4.3 Audio Denoising 38811.5 Exercises 394References 394Index 401

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 viiiPreface for the Second Edition ixPreface for the First Edition x1 Introduction 1U Zölzer1.1 Continuous-time Signals and Convolution 11.2 Continuous-time Fourier Transform and Laplace Transform 61.3 Sampling and Reconstruction 61.4 Discrete-time Signals and Convolution 81.5 Discrete-time Fourier Transform and Z-Transform 111.6 Discrete Fourier Transform 111.7 FIR and IIR Filters 121.8 Adaptive Filters 181.9 Exercises 21References 232 Quantization 25U Zölzer2.1 Signal Quantization 252.1.1 Classical Quantization Model 252.1.2 Quantization Theorem 282.1.3 Statistics of Quantization Error 342.2 Dither 402.2.1 Basics 402.2.2 Implementation 442.2.3 Examples 442.3 Spectrum Shaping of Quantization – Noise Shaping 462.4 Number Representation 512.4.1 Fixed-point Number Representation 522.4.2 Floating-point Number Representation 572.4.3 Effects on Format Conversion and Algorithms 602.5 JS Applet – Quantization, Dither, and Noise Shaping 622.6 Exercises 64References 653 Sampling Rate Conversion 67U Zölzer3.1 Basics 673.1.1 Upsampling and Anti-Imaging Filtering 683.1.2 Downsampling and Antialiasing Filtering 693.2 Synchronous Conversion 703.3 Asynchronous Conversion 743.3.1 Single-stage Methods 763.3.2 Multistage Methods 783.3.3 Control of Interpolation Filters 803.4 Interpolation Methods 833.4.1 Polynomial Interpolation 833.4.2 Lagrange Interpolation 853.4.3 Spline Interpolation 873.5 Exercises 94References 954 AD/DA Conversion 97U Zölzer4.1 Methods 974.1.1 Nyquist Sampling 974.1.2 Oversampling 984.1.3 Delta-sigma Modulation 1004.2 AD Converters 1134.2.1 Specifications 1134.2.2 Parallel Converter 1164.2.3 Successive Approximation 1174.2.4 Counter Methods 1184.2.5 Delta-sigma AD Converter 1204.3 DA Converters 1204.3.1 Specifications 1214.3.2 Switched Voltage and Current Sources 1234.3.3 Weighted Resistors and Capacitors 1244.3.4 R–2R Resistor Networks 1264.3.5 Delta-sigma DA Converter 1274.4 JS Applet – Oversampling and Quantization 1274.5 Exercises 129References 1305 Audio Processing Systems 131U Zölzer and D Ahlers5.1 Digital Signal Processors 1325.1.1 Fixed-point DSPs 1325.1.2 Floating-point DSPs 1335.2 Digital Audio Interfaces 1335.2.1 Two-channel AES/EBU Interface 1345.2.2 MADI Interface 1355.2.3 Audio in HDMI 1395.2.4 Audio Computer Interfaces 1405.2.5 Audio Network Interfaces 1415.3 Two-channel Systems 1465.4 Multi-channel Systems 146References 1476 Equalizers 149U Zölzer6.1 Basics 1496.2 Recursive Audio Filters 1536.2.1 Design 1536.2.2 Parametric Filter Structures 1626.2.3 Quantization Effects 1726.3 Non-recursive Audio Filters 1906.3.1 Basics of Fast Convolution 1916.3.2 Fast Convolution of Long Sequences 1946.3.3 Filter Design by Frequency Sampling 2016.4 Multi-complementary Filter Bank 2026.4.1 Principles 2036.4.2 Example: Eight-band Multi-complementary Filter Bank 2086.5 Delay-based Audio Effects 2146.6 JS Applet – Audio Filters 2156.7 Exercises 217References 2207 Room Simulation 225U Zölzer, P Nowak, and P Bhattacharya7.1 Basics 2257.1.1 Room Acoustics 2257.1.2 Model-based Room Impulse Responses 2277.1.3 Measurement of Room Impulse Responses 2307.1.4 Simulation of Room Impulse Responses 2347.2 Early Reflections 2357.2.1 Ando’s Investigations 2357.2.2 Gerzon Algorithm 2367.3 Subsequent Reverberation 2417.3.1 Schroeder Algorithm 2417.3.2 General Feedback Systems 2497.3.3 Feedback Allpass Systems 2527.4 Approximation of Room Impulse Responses 2567.5 JS Applet – Fast Convolution 2587.6 Exercises 259References 2608 Dynamic Range Control 265U Zölzer and E Gerat8.1 Basics 2658.2 Static Curve 2668.3 Dynamic Behavior 2698.3.1 Level Measurement 2698.3.2 Gain Factor Smoothing 2728.3.3 Time Constants 2728.4 Implementation 2738.4.1 Limiter 2738.4.2 Compressor 2748.4.3 Compressor, Expander, Noise Gate 2768.4.4 Combination System 2768.5 Realization Aspects 2788.5.1 Sampling Rate Reduction 2788.5.2 Curve Approximation 2798.5.3 Stereo Processing 2808.6 Multiband DRC 2808.7 Dynamic Equalizers 2818.8 Source-filter DRC 2838.8.1 Introduction 2838.8.2 Combination with DRC 2848.8.3 Applications 2848.9 JS Applet – Dynamic Range Control 2878.10 Exercises 288References 2899 Audio Coding 291U Zölzer and P Bhattacharya9.1 Lossless Audio Coding 2919.2 Lossy Audio Coding 2939.3 Psychoacoustics 2959.3.1 Critical Bands and Absolute Threshold 2959.3.2 Masking 2979.4 ISO-MPEG1 Audio Coding 3039.4.1 Filter Banks 3039.4.2 Psychoacoustic Models 3059.4.3 Dynamic Bit Allocation and Coding 3099.5 MPEG-2 Audio Coding 3109.6 MPEG-2 Advanced Audio Coding 3109.7 MPEG-4 Audio Coding 3219.8 Spectral Band Replication 3259.9 Constrained Energy Lapped Transform – Gain and Shape Coding 3279.9.1 Gain Quantization 3299.9.2 Shape Quantization 3309.9.3 Range Coding 3319.9.4 CELT Decoding 3329.10 JS Applet – Psychoacoustics 3339.11 Exercises 333References 33410 Nonlinear Processing 341M Holters and L Köper10.1 Fundamentals 34110.2 Overdrive, Distortion, Clipping 34310.3 Nonlinear Filters 34710.4 Aliasing and its Mitigation 35010.5 Virtual Analog Modeling 35410.5.1 Wave Digital Filters 35510.5.2 State-space Approaches 35910.6 Exercises 363References 36411 Machine Learning for Audio 367P Bhattacharya, P Nowak, and U Zölzer11.1 Introduction 36711.2 Unsupervised and Supervised Learning 36811.3 Gradient Descent and Backpropagation 36911.3.1 Feedforward Artificial Neural Network 36911.3.2 Convolutional Neural Network 37311.4 Applications 37511.4.1 Parametric Filter Adaptation 37511.4.2 Room Simulation 38311.4.3 Audio Denoising 38811.5 Exercises 394References 394Index 401

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 viiiPreface for the Second Edition ixPreface for the First Edition x1 Introduction 1U Zölzer1.1 Continuous-time Signals and Convolution 11.2 Continuous-time Fourier Transform and Laplace Transform 61.3 Sampling and Reconstruction 61.4 Discrete-time Signals and Convolution 81.5 Discrete-time Fourier Transform and Z-Transform 111.6 Discrete Fourier Transform 111.7 FIR and IIR Filters 121.8 Adaptive Filters 181.9 Exercises 21References 232 Quantization 25U Zölzer2.1 Signal Quantization 252.1.1 Classical Quantization Model 252.1.2 Quantization Theorem 282.1.3 Statistics of Quantization Error 342.2 Dither 402.2.1 Basics 402.2.2 Implementation 442.2.3 Examples 442.3 Spectrum Shaping of Quantization – Noise Shaping 462.4 Number Representation 512.4.1 Fixed-point Number Representation 522.4.2 Floating-point Number Representation 572.4.3 Effects on Format Conversion and Algorithms 602.5 JS Applet – Quantization, Dither, and Noise Shaping 622.6 Exercises 64References 653 Sampling Rate Conversion 67U Zölzer3.1 Basics 673.1.1 Upsampling and Anti-Imaging Filtering 683.1.2 Downsampling and Antialiasing Filtering 693.2 Synchronous Conversion 703.3 Asynchronous Conversion 743.3.1 Single-stage Methods 763.3.2 Multistage Methods 783.3.3 Control of Interpolation Filters 803.4 Interpolation Methods 833.4.1 Polynomial Interpolation 833.4.2 Lagrange Interpolation 853.4.3 Spline Interpolation 873.5 Exercises 94References 954 AD/DA Conversion 97U Zölzer4.1 Methods 974.1.1 Nyquist Sampling 974.1.2 Oversampling 984.1.3 Delta-sigma Modulation 1004.2 AD Converters 1134.2.1 Specifications 1134.2.2 Parallel Converter 1164.2.3 Successive Approximation 1174.2.4 Counter Methods 1184.2.5 Delta-sigma AD Converter 1204.3 DA Converters 1204.3.1 Specifications 1214.3.2 Switched Voltage and Current Sources 1234.3.3 Weighted Resistors and Capacitors 1244.3.4 R–2R Resistor Networks 1264.3.5 Delta-sigma DA Converter 1274.4 JS Applet – Oversampling and Quantization 1274.5 Exercises 129References 1305 Audio Processing Systems 131U Zölzer and D Ahlers5.1 Digital Signal Processors 1325.1.1 Fixed-point DSPs 1325.1.2 Floating-point DSPs 1335.2 Digital Audio Interfaces 1335.2.1 Two-channel AES/EBU Interface 1345.2.2 MADI Interface 1355.2.3 Audio in HDMI 1395.2.4 Audio Computer Interfaces 1405.2.5 Audio Network Interfaces 1415.3 Two-channel Systems 1465.4 Multi-channel Systems 146References 1476 Equalizers 149U Zölzer6.1 Basics 1496.2 Recursive Audio Filters 1536.2.1 Design 1536.2.2 Parametric Filter Structures 1626.2.3 Quantization Effects 1726.3 Non-recursive Audio Filters 1906.3.1 Basics of Fast Convolution 1916.3.2 Fast Convolution of Long Sequences 1946.3.3 Filter Design by Frequency Sampling 2016.4 Multi-complementary Filter Bank 2026.4.1 Principles 2036.4.2 Example: Eight-band Multi-complementary Filter Bank 2086.5 Delay-based Audio Effects 2146.6 JS Applet – Audio Filters 2156.7 Exercises 217References 2207 Room Simulation 225U Zölzer, P Nowak, and P Bhattacharya7.1 Basics 2257.1.1 Room Acoustics 2257.1.2 Model-based Room Impulse Responses 2277.1.3 Measurement of Room Impulse Responses 2307.1.4 Simulation of Room Impulse Responses 2347.2 Early Reflections 2357.2.1 Ando’s Investigations 2357.2.2 Gerzon Algorithm 2367.3 Subsequent Reverberation 2417.3.1 Schroeder Algorithm 2417.3.2 General Feedback Systems 2497.3.3 Feedback Allpass Systems 2527.4 Approximation of Room Impulse Responses 2567.5 JS Applet – Fast Convolution 2587.6 Exercises 259References 2608 Dynamic Range Control 265U Zölzer and E Gerat8.1 Basics 2658.2 Static Curve 2668.3 Dynamic Behavior 2698.3.1 Level Measurement 2698.3.2 Gain Factor Smoothing 2728.3.3 Time Constants 2728.4 Implementation 2738.4.1 Limiter 2738.4.2 Compressor 2748.4.3 Compressor, Expander, Noise Gate 2768.4.4 Combination System 2768.5 Realization Aspects 2788.5.1 Sampling Rate Reduction 2788.5.2 Curve Approximation 2798.5.3 Stereo Processing 2808.6 Multiband DRC 2808.7 Dynamic Equalizers 2818.8 Source-filter DRC 2838.8.1 Introduction 2838.8.2 Combination with DRC 2848.8.3 Applications 2848.9 JS Applet – Dynamic Range Control 2878.10 Exercises 288References 2899 Audio Coding 291U Zölzer and P Bhattacharya9.1 Lossless Audio Coding 2919.2 Lossy Audio Coding 2939.3 Psychoacoustics 2959.3.1 Critical Bands and Absolute Threshold 2959.3.2 Masking 2979.4 ISO-MPEG1 Audio Coding 3039.4.1 Filter Banks 3039.4.2 Psychoacoustic Models 3059.4.3 Dynamic Bit Allocation and Coding 3099.5 MPEG-2 Audio Coding 3109.6 MPEG-2 Advanced Audio Coding 3109.7 MPEG-4 Audio Coding 3219.8 Spectral Band Replication 3259.9 Constrained Energy Lapped Transform – Gain and Shape Coding 3279.9.1 Gain Quantization 3299.9.2 Shape Quantization 3309.9.3 Range Coding 3319.9.4 CELT Decoding 3329.10 JS Applet – Psychoacoustics 3339.11 Exercises 333References 33410 Nonlinear Processing 341M Holters and L Köper10.1 Fundamentals 34110.2 Overdrive, Distortion, Clipping 34310.3 Nonlinear Filters 34710.4 Aliasing and its Mitigation 35010.5 Virtual Analog Modeling 35410.5.1 Wave Digital Filters 35510.5.2 State-space Approaches 35910.6 Exercises 363References 36411 Machine Learning for Audio 367P Bhattacharya, P Nowak, and U Zölzer11.1 Introduction 36711.2 Unsupervised and Supervised Learning 36811.3 Gradient Descent and Backpropagation 36911.3.1 Feedforward Artificial Neural Network 36911.3.2 Convolutional Neural Network 37311.4 Applications 37511.4.1 Parametric Filter Adaptation 37511.4.2 Room Simulation 38311.4.3 Audio Denoising 38811.5 Exercises 394References 394Index 401