Reassigned Scalograms and Singularities
Eric Chassande-Mottin, Patrick Flandrin · Birkhäuser Basel eBooks · 2001
Reassignment is a general nonlinear technique aimed at increasing the localization of time-frequency and time-scale distributions. Its principle consists in supplementing an energy distribution with a suitable vector field, thanks to which energy contributions are moved on the plane so as to sharpen the initial distribution. Reassignment can be performed in an efficient way and, in the case of scalograms (i.e., wavelet-based energy densities), it can be equipped with fast algorithms too. When applied to isolated Hölder singularities, scalogram reassignment acts as a squeezing operator upon the influence cone of the underlying wavelet transform, thus permitting a sharper localization and a higher contrast as compared to conventional scalograms. Closed form expressions can be obtained for the specific family of Klauder wavelets, with the Morlet wavelet as a limiting case. When considered as a function of scale at the time instant of the singularity, reassigned scalograms are shown to undergo a power-law evolution from which the Hölder exponent can be estimated. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.