Mathematics of the Discrete Fourier Transform (DFT): with Audio Applications ---- Second Edition

Julius O. Smith III 2007

Detailed derivation of the Discrete Fourier Transform (DFT) and its associated mathematics, including elementary audio signal processing applications and matlab programming examples.


Introduction to Digital Filters: with Audio Applications

Julius O. Smith III 2007

A digital filter can be pictured as a “black box” that accepts a sequence of numbers and emits a new sequence of numbers. In digital audio signal processing applications, such number sequences usually represent sounds. For example, digital filters are used to implement graphic equalizers and other digital audio effects. This book is a gentle introduction to digital filters, including mathematical theory, illustrative examples, some audio applications, and useful software starting points. The theory treatment begins at the high-school level, and covers fundamental concepts in linear systems theory and digital filter analysis. Various “small” digital filters are analyzed as examples, particularly those commonly used in audio applications. Matlab programming examples are emphasized for illustrating the use and development of digital filters in practice.


Physical Audio Signal Processing: for Virtual Musical Instruments and Digital Audio Effects

Julius O. Smith III 2010

This book describes signal-processing models and methods that are used in constructing virtual musical instruments and audio effects. Specific topics considered include delay effects such as phasing, flanging, the Leslie effect, and artificial reverberation; virtual acoustic musical instruments such as guitars, pianos, bowed strings, woodwinds, and brasses; and various component technologies such as digital waveguide modeling, wave digital modeling, commuted synthesis, resonator factoring, feedback delay networks, digital interpolation, Doppler simulation, nonlinear elements, finite difference schemes, passive signal processing, and associated software.


Spectral Audio Signal Processing

Julius O. Smith III 2011

Spectral Audio Signal Processing is the fourth book in the music signal processing series by Julius O. Smith. One can say that human hearing occurs in terms of spectral models. As a result, spectral models are especially useful in audio applications. For example, with the right spectral model, one can discard most of the information contained in a sound waveform without changing how it sounds. This is the basis of modern audio compression techniques. The chapters are organized in a progression from basic spectrum analysis to more advanced frequency-domain signal processing as follows: * Fourier transforms and theorems * Spectrum analysis windows and their design * FIR digital filter design * Spectrum analysis of sinusoids * Spectrum analysis of noise * Time-frequency displays * The Short-Time Fourier Transform (STFT) * Overlap-add STFT processing * Filter-bank view of the STFT * Applications of the STFT * Multirate polyphase and wavelet filter banks In addition, appendices are provided containing material that extends and supplements various chapters in various directions. Others provide supporting background material: * Notation * Continuous-time Fourier theorems * Statistical signal processing * Gaussian function properties * Bilinear audio frequency warping * Matlab examples * History of spectral modeling by topic