Hybrid Modelling of an Audio Signal Based on 1-D Wold Decomposition

Abstract

This paper presents a hybrid model which is applicable to a wide variety of unidimensional signals like speech and more complex audio signals. We propose a new criterion for an optimal reconstruction of an unidimensional signal based on Wold-like decomposition of the stochastic processes. This decomposition inthe case 1D implies two mutually orthogonal parts: a purely indeterministic part and a deterministic part, which can be modelled respectively by an autoregressive model and by a harmonic model. The problem to which we answer is the identification and the separation of the two parts, by a new criterion which combines the quality and the parsimony of the parametric representations. Both analytical and experimental results show that the deterministic part and completely non-deterministic components should be parametrized separately. The model proposed by us is very efficient in terms of the numbers of parameters used in the reconstruction of the original signal.