This toolkit implements several related transforms and their inverses:

  • Modified Discrete Cosine Transform (MDCT)
  • Modified Discrete Sine Transform (MDST)
  • Modulated Complex Lapped Transform (MCLT) aka Complex Modified Discrete Cosine Transform (CMDCT)

All transforms are implemented as

  • the complete lapped transform, along with windowing and time domain aliasing cancellation (TDAC) reconstruction and
  • the core un-windowed standalone transform.

All transforms are implemeted in

  •,a fast, FFT-based method (for actual use), see [Bosi]
  • mdct.slow, a slow, pure-Python fashion (for testing) and


Warning is exposed as mdct. Please use this module directly.

import mdct
spec = mdct.mdct(signal)
output = mdct.imdct(spec)

Indices and tables

[Bosi]Marina Bosi, Richard E. Goldberg and Leonardo Chiariglione, “Introduction to Digital Audio Coding and Standards”, Kluwer Academic Publishers, 01 December, 2002.