Discrete rotational Gabor transform

Abstract

In this paper, we present a discrete rotational Gabor transform and apply it to signal representation on a non-rectangular time-frequency plane tiling. We use a modified version of the recently proposed discrete rotational Fourier transform. The rotational Gabor transform decomposes a signal using as basis functions scaled, translated and modulated by linear chirps windows. As a result, the time-varying frequency content of a signal is represented better than with sinusoidal modulated expansions. For a multi-component signal, the Gabor coefficients are obtained by combining different tilings to maximize a local energy concentration measure. This permits us to achieve a highly localized time-frequency signal representation. Examples are given to illustrate the transformation.