Regionally optimised time-frequency distributions using finite mixture models

Amethod 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 involves the determination of the parameters of a finite mixture of Gaussians, which is used to model an initial time-frequency distribution. The expectation-maximisation algorithm and the functional merging technique are used to derive the parameter set, including the number of Gaussians in the mixture. The mixture model indicates the number of (linear) components in the signal, and the regions they occupy in the time-frequency plane. This information is used to isolate the components, and smoothing kernels are designed using the properties of each isolated component. During the generation of the smoothing kernels, a set of basis functions is derived for each component, which describes the time-frequency region it occupies. This basis can be used for time-frequency filtering, enabling operations such as signal decomposition and noise reduction to be performed.