Acoustic Models: Fourier Transform

Links

• Tutorial: "The DFT a Pied - Mastering Fourier in One Day" Stephen M. Bernsee's excellent introduction to the Fourier Transform.
• Mathematics of the Discrete Fourier Transform (DFT) with Audio Applications Julius Smith's book. Fairly math intensive.

Applications and Examples

• SoundHack Phase vocoder and additional spectral processing, written by Tom Erbe. For MacOS only.
• POWERpv Eric Lyon's phase vocoder package. Also see Eric Lyon's homepage.
• PVNation and Hyperupic Applications by Christopher Penrose. PVNation is a command line phase vocoder package. Hyperupic was inspired by the UPIC system, a system for realizing sound from graphic tablets envisioned by Iannis Xenakis. Try it out.
• FFTease Spectral processing objects for MaxMSP by Eric Lyon and Christopher Penrose. Includes and number of unique algorithms for spectral manipulation.
• PVC Paul Koonce's command line phase vocoder. Also check out PVCX, a MacOS X GUI front end for PVC.

• FFTtheory.pdf
  Michael's class notes