Filter design for linear frequency modulation signal based on fractional Fourier transform

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Abstract
The fractional Fourier transform (FRFT) can transform the linear frequency modulation (LFM) signal into delta function for a proper orders, since the kernel of FRFT has a property of LFM. Using this property, the paper proposes the filter for LFM signal with noise, which avoids cross-term of quadratic distribution due to the linearity of FRFT. The method can reduce noise by optimizing the parameter p in (p, u) plane. The filtering performance is regulated by the correlation coefficient, and evaluated by mean square error (MSE). Computer simulations show that the proposed algorithm can filter the signals well compared to the pseudo Wigner Ville distribution for avoiding the cross-term problem. The statistical analysis of the MSE is also given for different signal to noise ratio, which illustrates the proposed algorithm has a rather good performance.

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