Signal Separation in the Wigner Distribution Domain Using Fractional Fourier Transform

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Executive Summary

In this paper the authors propose an algorithm based on the fractional Fourier transform to separate the different components of a signal in the Wigner time-frequency domain. The aim is to obtain a compressed representation for such a signal containing a minimal number of parameters. The proposed procedure gets rid of the noise and the cross-terms after separating the signal components. Assuming the signals under consideration have chirps and sinusoids, the fractional Fourier transform is used to rotate the components to obtain a sinusoidal or impulsive sparse representation. The procedure relies on filtering or windowing after obtaining the order of the fractional Fourier transform for each of the components.

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