Chapter 11. Time and Frequency Warping Musical Signals

  1. Udo Zölzer
  1. G. Evangelista

Published Online: 30 JUL 2004

DOI: 10.1002/047085863X.ch11

DAFX: Digital Audio Effects

DAFX: Digital Audio Effects

How to Cite

Evangelista, G. (2002) Time and Frequency Warping Musical Signals, in DAFX: Digital Audio Effects (ed U. Zölzer), John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/047085863X.ch11

Editor Information

  1. University of the Federal Armed Forces Hamburg, Germany

Author Information

  1. Swiss Federal Institute of Technology Lausanne (EPFL), Switzerland

Publication History

  1. Published Online: 30 JUL 2004
  2. Published Print: 31 MAR 2002

ISBN Information

Print ISBN: 9780471490784

Online ISBN: 9780470858639



  • time warping;
  • frequency warping;
  • signal representations;
  • transforms;
  • Fourier transforms;
  • Laguerre transforms


In this chapter we describe interesting audio effects that can be obtained by deforming the time and/or the frequency axis. Time warping aims at deforming the waveform or the envelope of the signal while frequency warping modifies its spectral content, e.g., by transforming an harmonic signal into an inharmonic one or vice-versa. The effects obtained by warping often increase the richness of the signal by introducing detuning or fluctuation of the waveform. The chapter is divided into two main parts. First we describe the time and frequency warping operations and derive algorithms for computing these effects. In the second part we illustrate some of their musical applications based on examples and case studies. Applications are presented for pitch shifting inharmonic sounds, inharmonizer, extraction of excitation signals, morphing and classical effects.


  • Introduction

  • Time Warping

    • Frequency Warping

    • Algorithms for Warping

    • Short-time Warping and Real-time Implementation

    • Time-varying Frequency Warping

  • Musical Uses of Warping

    • Pitch Shifting Inharmonic Sounds

    • Inharmonizer

    • Comb Filtering+Warping and Extraction of Excitation Signals in Inharmonic Sounds

    • Vibrato, Glissando, Trill and Flatterzunge

    • Morphing

  • Conclusion

  • Bibliography