Regionally optimised kernels for time-frequency distributions

Ideally, kernels used to generate bilinear time-frequency distributions (TFD) should be signal-dependent, and optimised independently at every location in the time-frequency (TF) plane. This poses an extremely severe computational burden. A compromise is proposed in this paper: time-varying kernels are optimised for specific regions in the time-frequency plane. The regions, designed to isolate separate components comprising the signal, are determined by modelling the TFD using a finite mixture model of Gaussian distributions. The parameters of the model are estimated using a combination of the expectation-maximisation algorithm and functional merging. The regional optimisation provides improved separation and resolution of closely-spaced components when compared to methods using a solely time-varying kernel, without incurring an overwhelming computational expense