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 time–frequency 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 time–frequency representation for multi-component signals. The proposed expansion uses the discrete fractional Fourier kernel and generates a parallelogram-shaped time–frequency 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.