A discrete fractional Gabor expansion for multi-component signals
Gabor expansion is widely used to represent the time-varying frequency content of non-stationary signals. Recently, new representations are presented on a general non-rectangular timefrequency grid. In this paper, we present a closed-form, discrete fractional Gabor expansion and show that it can be used to estimate a high resolution timefrequency representation for multi-component signals. The proposed expansion uses the discrete fractional Fourier kernel and generates a parallelogram-shaped timefrequency plane tiling. Completeness and biorthogonality conditions of the new expansion are derived. We also present a search algorithm to obtain optimal analysis fraction orders for the compact representation of multi-component signals.
fractional gabor expansion discrete gabor expansion fractional fourier transform