化学信号的近似高阶导数计算

Approximate High Order Derivative Calculation of Analytical Signals

提出了化学信号近似四阶导数计算的新方法———小波卷积法。该法通过信号与二阶样条小波函数的卷积运算对信号求导,能用于高噪音信号的直接求导,避免了普通导数运算将噪音放大的缺陷,即使对信噪比低至0.5的信号也能得到光滑的导数信号。详细讨论了尺度值、噪音、信号类型对求导的影响并建立了参数确定规则。将该法用于含噪音重叠分析化学信号的求导,能同时提高信号的分辨率和信噪比,结果满意。

A novel method for approximate fourth derivative calculation of analytical signal called wavelet convolution method is proposed and successfully used in processing CE signals. In this method, the derivative signals are produced by convoluting 2nd-order spline wavelet function with the original signals. It can process noisy signals efficiently, and smooth derivative signals are obtained. The influence of scale, noise level and signal types are discussed, and the rule for determination of parameter is found. When the method is used to calculate derivative of overlapped signals with high noise, both separation degree and signal-noise-ratio can be improved greatly.