Multi-window Gabor expansion for evolutionary spectral analysis

Abstract

In this paper, we connect a new multi-window discrete Gabor expansion of finite extent, deterministic signals with their evolutionary spectra. In our method both the signal representation and its corresponding evolutionary spectrum are obtained simultaneously. Including a scale parameter in the discrete Gabor expansion, we develop a multi-window representation which can be related to the deterministic version of the Wold-Cramer decomposition of non-stationary signals. By choosing Gaussian windows and appropriate scales, the expansion can be used to represent the narrow- and wide-band components of a signal. The evolutionary spectrum is then easily calculated from the Gabor coefficients. The computation of the evolutionary spectrum using this approach can be efficiently done by means of the Fast Fourier Transform algorithm. As an application, we present an approximate implementation of time-frequency masking. This implementation only requires that the support of the Gabor coefficients be restricted in the time-frequency plane. Examples illustrating the evolutionary spectral analysis and the proposed time-frequency masking are given.