信号去噪的一种优化算法

信号去噪通常是通过低通滤波器来实现的 ,但线性滤波在高精度场合并不能满足要求。为此提出了一种可给出信号高精度估计的非线性方法 ,分析了信号k阶导数的特点和噪声特性 ,在平稳时间序列的高阶差分对方差不变性的基础上 ,将信噪分离的参数估计问题转化为一类极值问题。利用矩阵理论分析了此类极值问题 ,给出了优化问题的解析解 ,并设计了相应算法。通过理论分析和实例验证了其有效性 ,并与最小二乘法作了比较

A New Signal Denoising Method Based on Data Property

Generally, a low pass filter is adopted to denoise the signal, however a linear filter can not provide results with high precision in many cases. In this paper a novel nonlinear method is proposed to meet the precision demand based on the separation technique in frequency domain. After the features of high order derivatives of signal and noise in observed data are analyzed the problem of separating signal from noise is converted into an extremum problem, with the high order difference of stationary time series invariant to the variance. Furthermore, an analytical solution is presented with the matrix theory, and so is the related algorithm. Finally, the effectiveness of the optimization algorithm is verified and the method is compared with the least square method through theoretical analysis and simulation. It is shown that this method is applicable to data processing.