Time-frequency analysis and wavelet analysis are generally used for providing signal expansions that are suitable for various further tasks such as signal analysis, de-noising, compression, source separation, ... However, time-frequency analysis and wavelet analysis also provide efficient ways for constructing signals' transformations. They are modelled as linear operators that can be designed directly in the transformed domain, i.e. the time-frequency plane, or the time-scale half plane. Among these linear operators, transformations that are diagonal in the time-frequency or time scale spaces, i.e. that may be expressed by multiplications in these domains, deserve particular attention, as they are extremely simple to implement, even though their properties are not necessarily easy to control. This work is a first attempt for exploring such approaches in the context of the analysis and the design of sound signals. We study more specifically the transformations that may be interpreted as linear time-varying (LTV) systems (often called time-varying filters). It is known that under certain assumptions, the latter may be conveniently represented by pointwise multiplication with a certain time frequency transfer function in the time-frequency domain. The purpose of this work is to examine such representations in practical situations, and investigate generalizations. The originality of this approach for sound synthesis lies in the design of practical operators that can be optimized to morph a given sound into another one, at a very high sound quality.

Date Published: 20 September 2007
PDF: 15 pages
Proc. SPIE 6701, Wavelets XII, 670118 (20 September 2007); doi: 10.1117/12.732447

Published in SPIE Proceedings Vol. 6701:
Wavelets XII
Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editor(s)