Audio Programming

Prerequisite Topics
Suggested languages: Fourier transforms:
 * C / C++ - low level, high performance, can be used for writing VST plugins, game audio components (e.g. native Unity audio plugins, Wwise plugins)
 * PureData - high level, can be used for prototyping synths, sound design work
 * Linear algebra
 * Complex numbers and Euler's Formula

Books
These books are available for free online and can also be purchased as physical books:
 * Julius O. Smith III: Introduction to Digital Filters - general mathematical theory about digital signal processing
 * Julius O. Smith III: Mathematics of the Discrete Fourier Transform - mathematical theory about spectral analysis
 * Miller Puckette: Theory and Techniques of Electronic Music - concrete examples of audio synthesis and filters in PureData (graphical programming language)
 * Sophocles J. Orfanidis: Introduction to Signal Processing - general information about digital signal processing

Articles

 * DSPRelated - site with blog posts, books etc.

Example Source

 * Music-DSP Source Code Archive
 * Freeverb3VST DSP related useful sites and references - site with a bunch of links, some dead ones

People

 * Julius O. Smith III
 * Perry R. Cook
 * Miller Puckette