Gabor Wigner Transform based on fractional fourier transform for low signal to noise ratio signal detection

To settle the time-frequency analysis problem of multi-component Linear Frequency Modulation(LFM)signals in the presence of low signal to noise ratio, a method called Gabor Wigner Transform(GWT) based on Fractional Fourier Transform(FRFT) is proposed. GWT is a composition of Gabor Transform(GT) and Wigner-Ville Distribution(WVD), hence GWT takes the advantages of both transforms, high resolution of WVD and cross-terms free of GT, but the time-frequency concentration of GWT is lower than that of WVD, the introduction of FRFT is to further improve the time-frequency concentration. LFM signals present a good energy clustering just in the optimal order of FRFT domain, while the white noise will not appear energy clustering in any FRFT domain, so the method has good anti-noise. In the condition of white Gaussian noise, a series of simulations have proved the method not only eliminate the interference of cross terms, but also improve the time-frequency concentration.