Book on Edited by
Udo Zölzer |

**Chapter
11**

Time and
Frequency Warping Musical Signals |

*G. Evangelista*

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.

**Contents**

- 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 Sig-

nals in Inharmonic Sounds - Vibrato, Glissando, Trill and Flatterzunge
- Morphing

- Conclusion
- Bibliography

Keywords: Time Warping, Frequency Warping, Signal Representations, Transforms, Fourier Transforms, Laguerre Transforms