In this paper we propose an algorithm based on the fractional Fourier transfolin 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 transfolin 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 transfolin for each of the components. Simulation results show the effectiveness of this approach in extracting the linear chirps and sinusoids from the noise and in eliminating the cross-teens from the Wigner distribution.