Time Delay Model of Fractional Fourier Transform and the Application in Signal Filtering

Abstract

Various frequency bands of noises are contained in the actual signal. And it's difficult to eliminate the noise portion, which has a time delay and same spectrum with the original signal with conventional filtering methods. Based on the time delay and the multiplication delay characteristics of the fractional Fourier transform (FRFT), we put forward a FRFT time delay model, which can increase distance between the signal and the noise component. Through corresponding Fractional Fourier Transform to noise-containing signal, the distance between the signal and common frequency noises can be constantly increased within the transform domain, thus easily separating the noise component. The algorithm of the model can be simply deduced, easy realized and converged fast. In the experiment, we simulated the separating characteristics of the transform, and used the method to de-noise the grating signal. Compared with other traditional methods, we find that the FRFT acquired a better result.