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In this work, we present a multiple window evolutionary spectral analysis on a non-rectangular time-frequency lattice based on a discrete fractional Gabor expansion. The traditional Gabor expansion uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals such as speech, music, etc., require a more flexible, nonrectangular time-frequency lattice for a compact representation. The proposed method uses a set of basis functions that are related to the fractional Fourier basis and generates a parallelogram-shaped tiling. Simulation results are given to illustrate the performance of our algorithm.