Digital Audio Theory A Practical Guide

Digital Audio Theory: A Practical Guide bridges the fundamental concepts and equations of digital audio with their real-world implementation in an accessible introduction, with dozens of programming examples and projects. Starting with digital audio conversion, then segueing into filtering, and finally real-time spectral processing, Digital Audio Theory introduces the uninitiated reader to signal processing principles and techniques used in audio effects and virtual instruments that are found in digital audio workstations. Every chapter includes programming snippets for the reader to hear, explore, and experiment with digital audio concepts. Practical projects challenge the reader, providing hands-on experience in designing real-time audio effects, building FIR and IIR filters, applying noise reduction and feedback control, measuring impulse responses, software synthesis, and much more. Music technologists, recording engineers, and students of these fields will welcome Bennett’s approach, which targets readers with a background in music, sound, and recording. This guide is suitable for all levels of knowledge in mathematics, signals and systems, and linear circuits. Code for the programming examples and accompanying videos made by the author can be found on the companion website, DigitalAudioTheory.com.

1 Introduction 1.1 Describing audio signals 1.2 Digital audio basics 1.3 Describing audio systems 1.4 Further reading 1.5 Challenges 1.6 Project– audio playback 2 Complex vectors and phasors 2.1 Complex number representation and operations 2.2 Complex conjugates 2.3 Phasors 2.4 Beat frequencies 2.5 Challenges 2.6 Project– AM and FM synthesis Bibliography 3 Sampling 3.1 Phasor representation on the complex plane 3.2 Nyquist frequency 3.3 Time shift operators 3.4 Sampling a continuous signal 3.5 Jitter 3.6 Challenges Bibliography 4 Aliasing and reconstruction 4.1 Under-sampling 4.2 Predicting the alias frequency 4.3 Anti-aliasing filter 4.4 Reconstruction 4.5 Challenges 4.6 Project– aliasing Bibliography 5 Quantization 5.1 Quantization resolution 5.2 Audio buffers 5.3 Sample-and-hold circuit 5.4 Quantization error (eq) 5.5 Pulse code modulation 5.6 Challenges Bibliography 6 Dither 6.1 Signal-to-Error Ratio (SER) 6.2 SER at low signal levels 6.3 Applying dither 6.4 Triangular PDF dither 6.5 High-frequency dither 6.6 Challenges 6.7 Project– dither effects Bibliography 7 DSP basics 7.1 Time-shift operators 7.2 Time-reversal operator 7.3 Time scaling 7.4 Block diagrams 7.5 Difference equations 7.6 Canonical form 7.7 Challenges 7.8 Project– plucked string model Bibliography 8 FIR filters 8.1 FIR filters by way of example 8.2 Impulse response 8.3 Convolution 8.4 Cross-correlation 8.5 FIR filter phase 8.6 Designing FIR filters 8.7 Challenges 8.8 Project– FIR filters Bibliography 9 z-Domain 9.1 Frequency response 9.2 Magnitude response 9.3 Comb filters 9.4 z-Transform 9.5 Pole/zero plots 9.6 Filter phase response 9.7 Group delay 9.8 Challenges 10 IIR filters 10.1 General characteristics of IIR filters 10.2 IIR filter transfer functions 10.3 IIR filter stability 10.4 Second-order resonators 10.5 Biquadratic filters 10.6 Proportional parametric EQ 10.7 Forward-reverse filtering 10.8 Challenges 10.9 Project– resonator Bibliography 11 Impulse response measurements 11.1 Noise reduction through averaging 11.2 Capturing IRs with MLS 11.3 Capturing IRs with ESS 11.4 Challenges 11.5 Project– room response measurements Bibliography 12 Discrete Fourier transform 12.1 Discretizing a transfer function 12.2 Sampling the frequency response 12.3 The DFT and inverse discrete Fourier transform 12.4 Twiddle factor 12.5 Properties of the DFT 12.6 Revisiting sampling in the frequency domain 12.7 Frequency interpolation 12.8 Challenges 12.9 Project– spectral filtering 13 Real-time spectral processing 13.1 Filtering in the frequency domain 13.2 Windowing 13.3 Constant overlap and add 13.4 Spectrograms 13.5 Challenges 13.6 Project– automatic feedback control 14 Analog modeling 14.1 Derivation of the z-transform 14.2 Impulse invariance 14.3 Bilinear transformation 14.4 Frequency sampling 14.5 Non-linear modeling with ESS 14.6 Challenges Bibliography

Christopher L. Bennett is a Professor in the Music Engineering Technology program at the University of Miami, Frost School of Music. He conducts research, teaches, and publishes in the fields of digital audio, audio programming, transducers, acoustics, psychoacoustics, and medical acoustics.