Seminar: Frequency warping of signals by means of modified phase vocoder

For NYU Community

Speaker: Professor Gianpaolo Evangelista

Faculty Host: Professor Ivan Selesnick



In this talk we review the concepts associated to frequency warping and derive approximate algorithms suitable for real-time frequency warping of signals.

Frequency warping is a signal transformation obtained by remapping the frequency axis according to a prescribed law. While by far the most common application of the transformation is in filter design (Constantinides transformation), its use in audio signal processing and sound synthesis has been rediscovered. In recent applications the technique has been used in order to design perceptual filter banks or to dynamically change the frequency damping characteristics (loop filter) in the physical model of guitar strings. However, the most interesting implications of frequency warping rest on warping signals rather than filters, with applications in several directions, ranging from adapted signal representations to  physical models of stiff systems and from digital audio effects to expression tools.

In the mid 60's P. Broome introduced the Laguerre sequences. The set  gives rise to orthogonal signal expansions that can be computed in terms of a chain of all-pass filters. The expansion coefficients can be  interpreted as a frequency warped version of the original signal, with the  reconstruction formula equivalent to unwarping. The concept was subsequently employed by Oppenheim, Johnson and Braccini in order to perform non-uniform bandwidth spectral analysis based on a frequency warped DFT. In recent work we employed frequency warping and iterated frequency warping in the construction of arbitrary scale factor or perceptually based wavelets.

Moreover, an extension of Laguerre sequences leads to reversible time-varying frequency warping algorithms interesting in audio effects.

The computation of the Laguerre transform is intensive [O(N^2)] for a time-limited signal of N samples] and inherently non-causal.  Furthermore, the warping characteristics are constrained to belong to a one-parameter family of curves. However, new approximate algorithms are proposed  that make accurate real-time computation of frequency warping possible even with arbitrary warping maps. These algorithms are based on an analysis- synthesis filter bank pair derived by suitably modifying the phase vocoder structure.


Gianpaolo Evangelista received the laurea in physics (summa cum laude) from “Federico II” University of Naples, Italy, in 1984 and the M.Sc. and  Ph.D. degrees in electrical engineering from the University of California,  Irvine, in 1987 and 1990, respectively. In 1985-1986, he has been with the Centre d'Etudes de Mathématique et Acoustique Musicale (CEMAMu/CNET), Paris, France. In 1991-1994 he has been with the Microgravity Advanced  Research and Support (MARS) Center, Naples. In 1995 he joined “Federico II”  University of Naples as a researcher. In 1998-2002 he has been scientific adjunct  with the Laboratory for Audiovisual Communications, Swiss Federal Institute of Technology (EPFL), Lausanne, Switzerland, on leave from the “Federico  II” University of Naples, which he rejoined in 2002-2005 as assistant  professor.

Since 2005 he is professor at the Linköping University, Sweden where he heads the Sound Technology research group. He is the author or coauthor of about 100 journal or conference  papers and book chapters and has been principal investigator or participant in  several national and international (EU) research projects. He has been a recipient of the Fulbright fellowship. His interests include audio, music, and image processing; coding;  wavelets; and multirate signal processing.