Digital Audio Theory : A Practical Guide book cover
1st Edition

Digital Audio Theory
A Practical Guide

ISBN 9780367276539
Published December 28, 2020 by Focal Press
254 Pages 123 B/W Illustrations

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Book Description

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,

Table of Contents

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


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


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


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


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


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


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


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


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


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


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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.