本文選題：尋峰算法 + 小波閾值法去噪��； 參考：《淮北師范大學》2017年碩士論文

【摘要】：在物質(zhì)分析方法中,有些測量方法是通過測量和分析物質(zhì)對應(yīng)的峰的位置、高度或面積來分析物質(zhì)的性質(zhì)。為了高效、準確地檢測峰位、峰寬和峰高等信息,研究了基于小波的去噪方法、基于高斯擬合的峰信號重構(gòu)技術(shù)和導數(shù)結(jié)合拐點法尋峰技術(shù),并給出了在重金屬檢測和離子遷移譜檢測中應(yīng)用。小波變換是一種新興的信號處理方法,其核心思想源自短時傅里葉變換的窗口化分析,同時改進了短時傅里葉變換中窗函數(shù)無法自適應(yīng)時頻變化的缺點。本文首先比較了小波變換模極大值法,小波基的小波系數(shù)相關(guān)性法與小波閾值法,選擇了程序簡單、對于譜信號中的白噪聲及正弦噪聲干擾去噪效果良好的小波閾值法作為去噪算法,重點討論閾值與小波基的選取。在閾值的選取上參考了Donoho的軟閾值法并進行改進,相比固定的軟硬閾值法更加靈活。同時參考了大量小波基函數(shù)的特征,根據(jù)譜信號譜線與譜信號中常見噪聲的特點結(jié)合仿真實驗進行選優(yōu),通過對比SNR與RMSE值,得到適合譜信號濾波處理的幾種小波基以及分解尺度與消失矩選取的關(guān)系。然后討論了尋峰的常用幾種算法。對譜信號的分析過程中,關(guān)鍵技術(shù)就是定位每個峰的起始點和終點,然后根據(jù)峰位和峰形計算峰高與峰面積,有時還要對畸變峰進行重構(gòu)。本文主要介紹常用尋峰算法包括比較法、導數(shù)法、高斯擬合法、對稱零面積法和小波變換法的工作原理和特點。最后給出了尋峰算法在儀器設(shè)計上的應(yīng)用。一是導數(shù)結(jié)合拐點法在重金屬檢測中的應(yīng)用,研究了溶出峰的特點并設(shè)計了快速尋峰算法,并開發(fā)了三電極傳感器的恒電位儀電路,并給出了測試結(jié)果和主要參數(shù)。另一個應(yīng)用是高斯擬合結(jié)合小波降噪處理離子遷移譜峰信號,研究基于小波的離子遷移譜信號的去噪方法和基于高斯擬合方法的離子遷移譜信號的重構(gòu)技術(shù),能夠準確還原因為信號峰的重疊而消失的離子峰,能夠提高應(yīng)用離子遷移譜定性物質(zhì)種類的能力。
[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.
【學位授予單位】：淮北師范大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：TN911.6

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