Time-frequency analysis using time-dependent ARMA models

Abstract

This paper discusses the estimation of time-frequency representations of non-stationary signals, by means of ARMA (autoregressive moving-average) models with time-dependent coefficients. In order to allow the estimation of the model on a single realisation of the random signal, it is assumed that the coefficients are weighted sums of known functions, for instance polynomials, cosines. Two ARMA models will be discussed in this paper. The first one is a white noise driven ARMA model, which is rather usual. The second one has been designed for deterministic or speech-like signals and consists of a linear system driven by intermittent inputs with additive output (white) noise. The time-frequency representation of the signal is then obtained from the state-space realisation of the time-dependent model. After a description of the algorithms involved in both estimators, the paper focuses on a comparison of the two ARMA models on modulated sinusoids corrupted by white noise. This shows that these models behave equally well for high SNR (signal-to-noise ratio), but the deterministic model gives better results when the SNR decreases.