A Novel Fractional Filter Design and Cross-Term Elimination in Wigner Distribution

The second and the third sentences of the abstract are changed and the shorter abstract is given as follows. To recover the nonstationary signal in complicated noise environment without distortion, a novel general design of fractional filter is proposed and applied to eliminate the Wigner cross-term. A time-frequency binary image is obtained from the time-frequency distribution of the observed signal and the optimal separating lines are determined by the support vector machine (SVM) classifier where the image boundary extraction algorithms are used to construct the training set of SVM. After that, the parameters and transfer function of filter can be determined by the parameters of the separating lines directly in the case of linear separability or line segments after the piecewise linear fitting of the separating curves in the case of nonlinear separability. Without any prior knowledge of signal and noise, this method can meet the reliability and universality simultaneously for filter design and realize the global optimization of filter parameters by machine learning even in the case of strong coupling between signal and noise. Furthermore, it could completely eliminate the cross-term in Wigner-Ville distribution (WVD) and the time-frequency distribution we get in the end has high resolution and good readability even when autoterms and cross-terms overlap. Simulation results verified the efficiency of this method.