Regionally optimised time-frequency distributions using finite mixture models

A method is presented for the improvement of the resolution and clarity of bilinear time-frequency distributions generated from signals consisting of a number of approximately time-frequency disjoint components. The method in volves the determination of the parameters of a finite mixture of Gaussians . which is used to model an initial time-frequency distribution. The expect ation-maximisation algorithm and the functional merging technique are used to derive the parameter set, including the number of Gaussians in the mixtu re. The mixture model indicates the number of (linear) components in the si gnal, and the regions they occupy in the time-frequency plane. This informa tion is used to isolate the components, and smoothing kernels are designed using the properties of each isolated component. During the generation of t he smoothing kernels, a set of basis functions is derived for each componen t, which describes the time-frequency region it occupies. This basis can be used for time-frequency filtering, enabling operations such as signal deco mposition and noise reduction to be performed. (C) 1999 Elsevier Science B. V. All rights reserved.