Digital Audio Theory: A Practical Guide from Focal Press 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.
- 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 ChallengesBibliography
- 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
- 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