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
Biography
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.
"Your background in music, sound, and recording makes you a power-user of digital audio signal processors. Wouldn’t you like to understand what’s going on inside those converters, delays, filters and more? Don’t you want to know what to listen for when it’s time to choose which one to use? And don’t you sort of want to create your own FX? Me too. There is the calculus and coding way into this, and then there is Christopher Bennett’s way in. If you want to understand digital audio theory – to have mastery of the theories and intuition about the possibilities – you don’t need an engineering degree, you need this book."
Alex U. Case, Sound Recording Technology, University of Massachusetts Lowell, Past President of the Audio Engineering Society, and author of Sound FX: Unlocking the Creative Potential of Recording Studio Effects and Mix Smart: Pro Audio Tips for Your Multitrack Mix
"This book is part of a fresh approach to the challenges that aspiring audio programmers face. Rather than serving as a reference manual, Bennett presents Digital Audio Theory as part of a journey, supplementing the reading material with over 30 video tutorials and code samples. It is essential reading for anyone trying to understand the fundamentals of signal processing. The explanations are clear and well thought out – easy enough for those with a casual math background to follow along, but challenging enough to introduce concepts that reach beyond algorithms covered by other books. Highly recommended!"
Joshua Hodge, a.k.a. The Audio Programmer
