小波变换与寻峰重构算法在谱信号分析中的应用

发布时间：2018-06-29 11:03

本文选题：寻峰算法 + 小波阈值法去噪　；参考：《淮北师范大学》2017年硕士论文

【摘要】：在物质分析方法中,有些测量方法是通过测量和分析物质对应的峰的位置、高度或面积来分析物质的性质。为了高效、准确地检测峰位、峰宽和峰高等信息,研究了基于小波的去噪方法、基于高斯拟合的峰信号重构技术和导数结合拐点法寻峰技术,并给出了在重金属检测和离子迁移谱检测中应用。小波变换是一种新兴的信号处理方法,其核心思想源自短时傅里叶变换的窗口化分析,同时改进了短时傅里叶变换中窗函数无法自适应时频变化的缺点。本文首先比较了小波变换模极大值法,小波基的小波系数相关性法与小波阈值法,选择了程序简单、对于谱信号中的白噪声及正弦噪声干扰去噪效果良好的小波阈值法作为去噪算法,重点讨论阈值与小波基的选取。在阈值的选取上参考了Donoho的软阈值法并进行改进,相比固定的软硬阈值法更加灵活。同时参考了大量小波基函数的特征,根据谱信号谱线与谱信号中常见噪声的特点结合仿真实验进行选优,通过对比SNR与RMSE值,得到适合谱信号滤波处理的几种小波基以及分解尺度与消失矩选取的关系。然后讨论了寻峰的常用几种算法。对谱信号的分析过程中,关键技术就是定位每个峰的起始点和终点,然后根据峰位和峰形计算峰高与峰面积,有时还要对畸变峰进行重构。本文主要介绍常用寻峰算法包括比较法、导数法、高斯拟合法、对称零面积法和小波变换法的工作原理和特点。最后给出了寻峰算法在仪器设计上的应用。一是导数结合拐点法在重金属检测中的应用,研究了溶出峰的特点并设计了快速寻峰算法,并开发了三电极传感器的恒电位仪电路,并给出了测试结果和主要参数。另一个应用是高斯拟合结合小波降噪处理离子迁移谱峰信号,研究基于小波的离子迁移谱信号的去噪方法和基于高斯拟合方法的离子迁移谱信号的重构技术,能够准确还原因为信号峰的重叠而消失的离子峰,能够提高应用离子迁移谱定性物质种类的能力。
[Abstract]:In material analysis, some methods of measurement are used to analyze the properties of matter by measuring and analyzing the position, height or area of the corresponding peak. In order to detect the information of peak position, peak width and peak height efficiently and accurately, the wavelet denoising method, the peak signal reconstruction technology based on Gao Si fitting and the peak finding technique based on derivative and inflection point method are studied. The applications in heavy metal detection and ion transport spectrum detection are also given. Wavelet transform is a new signal processing method whose core idea is derived from window analysis of short time Fourier transform (STFT) and improves the shortcoming of window function which can not adapt to time frequency change in short time Fourier transform (STFT). In this paper, the modulus maximum method of wavelet transform, the correlation method of wavelet coefficients and the wavelet threshold method are compared, and the program is simple. For the white noise and sinusoidal noise in spectral signal, the wavelet threshold method is used as the denoising algorithm, and the selection of threshold and wavelet basis is discussed. Donoho's soft threshold method is referred to and improved in the selection of threshold, which is more flexible than the fixed soft and hard threshold method. At the same time, referring to the characteristics of a large number of wavelet basis functions, according to the characteristics of spectral lines and common noises in spectral signals, combined with the simulation experiments, the SNR and RMSE values are compared. Several wavelet bases suitable for spectral signal filtering and the relationship between decomposition scale and vanishing moment are obtained. Then several common algorithms for peak searching are discussed. In the process of spectrum signal analysis, the key technique is to locate the starting point and end point of each peak, then calculate the peak height and area according to the peak position and shape, and sometimes reconstruct the distortion peak. This paper mainly introduces the working principle and characteristics of common peak searching algorithms including comparison method, derivative method, Gao Si fitting method, symmetric zero area method and wavelet transform method. Finally, the application of peak finding algorithm in instrument design is given. The first is the application of derivative combined with inflection point method in heavy metal detection. The characteristics of dissolution peak are studied and a fast peak finding algorithm is designed. The potentiostat circuit of three-electrode sensor is developed, and the test results and main parameters are given. Another application is Gao Si fitting combined with wavelet denoising to deal with the peak signal of ion migration spectrum. The de-noising method of ion transport spectrum signal based on wavelet and the reconstruction technology of ion transport spectrum signal based on Gao Si fitting method are studied. It can accurately reduce the ion peaks which disappeared because of the overlapping of the signal peaks, and can improve the ability to use ion transport spectra to characterize the species of substances.
【学位授予单位】：淮北师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TN911.6

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