Abstract

Here we describe novel Bayesian models for time-frequency analysis of non-stationary audio waveforms. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of time-frequency shifted versions of a simple window function. Prior distributions over the corresponding time-frequency coefficients are constructed in a manner which favours both smoothness of the estimated function and sparseness of the coefficient representation (either indirectly through scale mixtures of normals, or directly through prior probability mass at zero). In this way prior regularisation may induce a parsimonious, meaningful representation of the underlying audio time series. 1. THE DISCRETE-TIME GABOR EXPANSION The discrete-time Gabor expansion of a periodic sequence f ∈ ℓ 2 (Z) having period L is given by f = M−1 � N−1 � m=0 n=0

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