Time-Scale Energy Distributions: A General Class
Olivier Rioul, Patrick Flandrin · 1992
This paper develops the theory of a new general class of signal energy representations depending on time and scale. Time-scale analysis has been introduced recently as a powerful tool through linear representations called (continu- ous) wavelet transforms (WT's), a concept for which we give an exhaustive bilinear generalization. Although time scale is presented as an alternative method to time frequency, strong links relating the two are emphasized, thus combining both de- scriptions into a unified perspective. We provide a full char- acterization of the new class: the result is expressed as an affine smoothing of the Wigner-Ville distribution, on which interest- ing properties may be further imposed through proper choices of the smoothing function parameters. Not only do specific choices allow recovering known definitions, but they also pro- vide, via separable smoothing, a continuous transition from Wigner-Ville to either spectrograms or scalograms (squared modulus of the WT). This property makes time-scale represen- tations a very flexible tool for nonstationary signal analysis.