Fractional Gabor spectral estimation for multi-component signals

Abstract

We present a high resolution time-frequency spectral analysis method for multi-component signals based on a discrete fractional Gabor expansion. The proposed discrete fractional Gabor expansion uses the closed form discrete fractional Fourier kernel and generate 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 an arbitrary, multi-component signal to estimate a high resolution Gabor spectrum.