A Novel Fractional Fourier Domain Filter Design Based on Time–Frequency Image Edge Detection

Abstract

To realize the lossless recovery of non-stationary signal in complicated noise environment, a novel design method of fractional Fourier domain filter is proposed assisted by time–frequency image edge detection. The time–frequency distribution of observed signal is obtained by Gabor-Wigner transform, and based on technique of image edge detection and selection algorithm, adjacent edge information of the different regions of in the time–frequency plane are obtained, which can be used to build support vector machine (SVM) training set. Respectively, for the two cases of linearly separable and inseparable signal and noise distribution, the separating line is drawn by the SVM separating algorithm and then the parameters of filter can be determined by the parameters of separating line. Simulation results show that without any prior knowledge of signal and noise, the design process can ensure the optimal performance of the filter and higher signal noise ratio is reached. Furthermore, an undistorted signal recovery is achieved even in the case of strong coupling between signal and noise, which proves the reliability, versatility and effectiveness of our filter design.