IEEE International Conference on Acoustics, Speech, and Signal Processing, Utah, United States Of America, 7 - 11 May 2001, pp.3529-3532
We present a fractional Gabor expansion on a general, nonrectangular time-frequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant bandwidth analysis results in a fixed, rectangular time frequency plane tiling. Many of the practical signals require a more flexible, non-rectangular time-frequency lattice for a compact representation. The proposed fractional Gabor expansion uses a set of basis functions that are related to the fractional Fourier basis and generate a non-rectangular tiling. The completeness and bi-orthogonality conditions of the new Gabor basis are discussed.