复合信号的分辨新技术

The measured system of analytical chemistry is general complex because of coexistence of some component in one system. So, the signal obtained from apparatus is compound signal containing noise. The resolution of complex signals is an active field of analytical chemistry. On the available signal, the common processing techniques (curve fitting, Fourier deconvolution and signal differential) and the newly presented methods (wavelet Fourier convolution and extracting certain detail information of signal's wavelet transform) can not meet the following expectation for resolution finely: (1) the degree of signal separation is raised and the peak widths are narrowed; (2) the peak positions are unchanged; (3) the peak areas correspond with the original signal; (4) baseline separation is achieved. Fourier deconvolution and signal differential also enlarge the noise of signal. In addition, Fourier deconvolution need do Fourier transform and inverse transform, curve fitting need iterative operation. These methods are so discommodious that their applications are limited in reality. This item focuses on the new resolution method for complex signal to solve these problems. The following new resolution techniques have been developed, which can meet the above expectation for resolution and the demands in practice.1、Resolution of overlapped peaks without noise--Spline Convolution (SC) In this method, the given signal is convoluted with a suitable resolving factor to separate the overlapped peaks. The resolving factor is the key of SC. We found that the factor can be made by any bell-like functions, such as spline function, gauss function, sine wave function and d(1/1+expx)/dx, in which the 3rd spline function and gauss function are the best. To make the peak positions unchanged after resolution, each peak position of resolving factor must correspond with the given signal. The peak position and peak number before resolution are determined by quadratic differential. The overlapped peaks whose degree is 0.5 can be separated successfully.2、Resolution of overlapped peaks with noise.(1) Spline Wavelet Self-convolution (SWSC).Construct the peak resoluter of spline wavelet by combining lowpass of spline wavelet transform with resolving factor. Because the peak resoluter contains the filter, noise in the original signal can be removed at the same time with resolving overlapped peaks. When signal-to-noise ratio (SNR) ≥20, the noise can be filtered on the whole. The filter of 3rd spline wavelet is used in SWSC.(2) Resolving high noise overlapped signals by Spline Wavelet Least Square (SWLS) .Regard the product of resolving factor and original signal as the processed signal in SWLS, to make it as a novel method that includes the capability of filter and resolution. Different resolving factors lead to different results and sine wave function is better, which is different from SWSC. For the complex signal whose SNR is lower than 1, the resolution and SNR of the processed signal by this method has been enhanced, and the noise is removed. The signal need to be processed by this method only once, no model is needed, very short time is cost, and the data point need not be 2n（n∈Z）. For processing noisy signal, SWSC is better when SNR >20, and SWLS is better when SNR<20.(3) Resolving overlapped signal by Continuous 2rd Spline Wavelet Transform (CSWT) CSWT is much better than continuous Marr wavelet transform, because Peak positions are determined accurately by CSWT even when the original signal has very high noise. First, find the position and width of each overlapped peak CSWT with a right scale; then separate the peaks by SWSC. This method can identify and resolve overlapped peaks automatically, can separate the overlapped peaks whose degree is as low as 0.57, can resolute overlapped peaks and filter noise (SNR is 2) at one time. The relative errors of peak area and position are less than ±5.0%. Moreover, the only parameter is scale, so there are no error and uncertainty owing to choosing of many parameters. CSWT is simple and its

创立小波自卷积法，应用小波构造一类峰分辨器，使其通过原信号的峰变窄，而峰位置和面积不变，并达到基线分离，真正实现重叠峰分辨。本法优于并行各法，只需一次通过峰分辨器即达到分辨，且是在时频范围内完成，处理前无需知道准确系统模型和统计特征，也无需对其中任何参数进行假设，计算快，储存省，是对复合信号分辨基数的新突破，意义重大。