Digital Audio Theory

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.

• 1 Introduction1.1 Describing audio signals1.2 Digital audio basics1.3 Describing audio systems1.4 Further reading1.5 Challenges1.6 Project – audio playback2 Complex vectors and phasors2.1 Complex number representation and operations2.2 Complex conjugates2.3 Phasors2.4 Beat frequencies2.5 Challenges2.6 Project – AM and FM synthesisBibliography3 Sampling3.1 Phasor representation on the complex plane3.2 Nyquist frequency3.3 Time shift operators3.4 Sampling a continuous signal3.5 Jitter3.6 ChallengesBibliography4 Aliasing and reconstruction4.1 Under-sampling4.2 Predicting the alias frequency4.3 Anti-aliasing filter4.4 Reconstruction4.5 Challenges4.6 Project – aliasingBibliography5 Quantization5.1 Quantization resolution5.2 Audio buffers5.3 Sample-and-hold circuit5.4 Quantization error (eq)5.5 Pulse code modulation5.6 ChallengesBibliography6 Dither6.1 Signal-to-Error Ratio (SER)6.2 SER at low signal levels6.3 Applying dither6.4 Triangular PDF dither6.5 High-frequency dither6.6 Challenges6.7 Project – dither effectsBibliography7 DSP basics7.1 Time-shift operators7.2 Time-reversal operator7.3 Time scaling7.4 Block diagrams7.5 Difference equations7.6 Canonical form7.7 Challenges7.8 Project – plucked string modelBibliography8 FIR filters8.1 FIR filters by way of example8.2 Impulse response8.3 Convolution8.4 Cross-correlation8.5 FIR filter phase8.6 Designing FIR filters8.7 Challenges8.8 Project – FIR filtersBibliography9 z-Domain9.1 Frequency response9.2 Magnitude response9.3 Comb filters9.4 z-Transform9.5 Pole/zero plots9.6 Filter phase response9.7 Group delay9.8 Challenges10 IIR filters10.1 General characteristics of IIR filters10.2 IIR filter transfer functions10.3 IIR filter stability10.4 Second-order resonators10.5 Biquadratic filters10.6 Proportional parametric EQ10.7 Forward-reverse filtering10.8 Challenges10.9 Project – resonatorBibliography11 Impulse response measurements11.1 Noise reduction through averaging11.2 Capturing IRs with MLS11.3 Capturing IRs with ESS11.4 Challenges11.5 Project – room response measurementsBibliography12 Discrete Fourier transform12.1 Discretizing a transfer function12.2 Sampling the frequency response12.3 The DFT and inverse discrete Fourier transform12.4 Twiddle factor12.5 Properties of the DFT12.6 Revisiting sampling in the frequency domain12.7 Frequency interpolation12.8 Challenges12.9 Project – spectral filtering13 Real-time spectral processing13.1 Filtering in the frequency domain13.2 Windowing13.3 Constant overlap and add13.4 Spectrograms13.5 Challenges13.6 Project – automatic feedback control14 Analog modeling14.1 Derivation of the z-transform14.2 Impulse invariance14.3 Bilinear transformation14.4 Frequency sampling14.5 Non-linear modeling with ESS14.6 ChallengesBibliography

"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