Fractional Fourier transform and time-frequency filtering

With the introduction of fast algorithms of the discrete fractional Fourier transform, its potential has been found in DSP, and several filtering algorithms have been proposed for some given signals. The meaning of the time-frequency filtering in the fractional Fourier domain for linear FM signal is analyzed to deal with the non-stability of this kind of signal, and the realization of the swept-frequency filter in the fractional Fourier domain is provided. On this basis, a multiplicative filter in the fractional Fourier domain is introduced. With the actual reverberation data and the LFM pulse for separation, good results are obtained: the Reverberation is largely removed, and a better performance is shown at a lower SRR.