Research On Peak Preservation And Smoothing Algorithms Of Derivative Spectrum

Derivative spectrum is the signal after derivation of the original signal.It can be used to identify spectral peaks and improve spectral resolution in many fields such as biology,chemistry and medicine.In most cases,the signal is often accompanied by noise,and the derivative is very sensitive to noise,so the noise of the derivative spectrum will be more serious.Therefore,smooth preprocessing is required.However,the smoothing operation is easy to cause the peaks to be weakened and difficult to recover,which will affect the subsequent peak detection or the analysis of substance content.Therefore,exploring peak-preserving smoothing algorithms has become a challenging task in derivative spectrum processing.Through literature analysis,it is found that the diffusion filter has better peak-preserving performance.Therefore,this paper first discusses the diffusion filter algorithm of the derivative spectrum.For this reason,this paper first discusses the diffusion filtering algorithm of derivative spectrum,in order to further smooth the noise in the flat region,based on the similarity of the signal segment,a piecewise classification derivative spectrum smoothing algorithm is proposed.Finally,the combination of fractional diffusion filtering and segmentation classification smoothing algorithm to achieve peak-preserving smoothing.The specific work content is as follows:1.Discuss the diffusion filter algorithm of derivative spectrum,including classic diffusion filter and time fractional order diffusion filter,give the numerical algorithm,and compare the specific signal with wavelet method and S-G method,and find the time fractional order diffusion filter has a good peak preservation effect.2.Based on the similarity of signal segments,a segmented classification derivative spectrum smoothing algorithm is proposed,and the basic idea and implementation process of the algorithm are given.Segment the derivative spectrum,then search for similar segments of each segment and form them into a two-dimensional array,then perform discrete cosine transform on the two-dimensional array,through shrinking the threshold,and then the inverse transformation is performed to obtain the smooth signal segment.Finally,the final smoothing signal is obtained by weighted averaging the smooth segment at the same position.Although in each section of the signal,the frequency of the real signal is lower than the frequency of the noise,and the high-frequency noise can be removed by the threshold shrinkage method,but it cannot effectively filter the noise in the same frequency band as the spectral peak,so the idea of quadratic smoothing is proposed,Specifically: 1.The smoothing results obtained by segmentation are smoothed again using conventional methods,and the improved effects of wavelet method,regularization method,S-G method and time fractional diffusion filter are discussed.2.Perform segmentation classification on the smoothing results obtained by segmentation classifying again,the similar classes are filtered by polynomial fitting,and compare their results.The research results show that the fractional diffusion model combined with the threshold contraction smoothing algorithm of segmentation classification has better peak-preserving smoothing performance.