基于支持向量机的信号滤波研究

提出了基于支持向量机（SVM）的信号滤波方法．由于利用了SVM泛化能力强、全局最优等特点，因此该方法与传统方法相比，能更有效地抑制随机加性噪声．在时域和频域分别讨论了参数对核函数的影响，通过对基于SVM的函数回归形式的变换，得出了一种能描述滤波原理的表达式．从该表达式中可以看出，核函数的作用相当于低通滤波，而其参数决定了滤波器的截止频率，从而可以通过对核函数参数进行优化，以取得最佳的滤波效果，达到抑制随机加性噪声的目的．仿真结果表明，基于SVM的滤波方法有效地抑制了随机加性噪声，为信号滤波提供了一种以结构风险最小化为理论框架的新手段．

Study on Signal Filtering Based on Support Vector Machine

A method for signal filtering based on support vector machine(SVM) was proposed.According to the excellent generalization performance and global optimal property for peak of SVM,the method can suppress the random additive noise more effectively in contrast with traditional ones.The effects of parameter on kernel function are analyzed in time domain and frequency domain respectively.According to the translation of form of regression based on SVM,an expression is obtained which can describe the principle of filtering.From the expression,a conclusion is drawn that the effect of kernel function is equivalent to that of low pass filter,and the cut-off(frequency) of it is determined by the parameter of kernel function.So an optimal effect of filtering can be reached by optimizing it's parameters to suppress the random additive noise.The simulation results show that the method based on SVM can suppress the additive random noise effectively,and presents a new way for signal filtering based on the theoretical framework of structural risk(minimization.)