Composite autoregressive system for sparse source-filter representation of speech

This paper presents a new generative model for speech signals called a ldquocomposite autoregressive systemrdquo. This model consists of a composite dictionary incorporating a set of the power spectral densities (PSDs) of excitation sources and a set of all-pole filters where the gain of each pair of excitation and filter elements is allowed to vary over time. We use this model to develop a computationally efficient scheme for generating a sparse mixture representation of speech based on the Expectation-Maximization algorithm. The algorithm iteratively updates the excitation PSDs and the gains through the update formulae, which reduce under a particular condition to the multiplicative update rule for non-negative matrix factorization with the Itakura-Saito distance criterion, and the all-pole parameters using the Levinson-Durbin algorithm.