优化Savitzky-Golay滤波器的参数及其在傅里叶变换红外气体光谱数据平滑预处理中的应用

对傅里叶变换中红外光谱数据的平滑预处理中，通常采用Savitzky-Golay滤波器的方法进行光谱数据的平滑预处理，然而Savitzky-Golay滤波器的多项式拟合阶次和窗宽等参数的合理选则始终是一个难题，并无统一的选择依据，通常在一定数值范围内，采用多组数据进行遍历尝试，最终选择一组相对较优的数据作为Savitzky-Golay滤波器的多项式拟合阶次和窗宽参数。文中探索了Savitzky-Golay滤波器的多项式拟合阶次和窗宽等参数的优化选取这一问题，并对其主要频率指标参数与多项式拟合阶次和窗宽等参数进行了定性定量分析，得出了截至频率、阻带起始点频率、第一旁瓣峰值频率及第一旁瓣峰值幅度与窗宽和阶次之间具体的计算方程表达式。随后，根据采集的中红外气体组分的光谱数据特征，依据上述计算方程式，优化计算选取多项式拟合阶次和窗宽分别为8和11时，其Savitzky-Golay滤波器的中红外气体组分的光谱数据平滑效果最优。最后通过实际采集的0.1%, 0.2%, 0.5%, 1%, 2%, 5%浓度的CH₄光谱数据进行平滑预处理，在次吸收峰区域，原始光谱的折算吸光率相对最大误差和最小误差分别为17.230 5%和0.243 0%， 平滑处理后的光谱的折算吸光率相对最大误差和最小误差分别为0.088 0%和0.020 6%。可见经过Savitzky-Golay滤波器进行所探索的光谱数据预处理之后其相对误差基本稳定，并且相对较低，为后期光谱数据的准确定性和定量分析奠定了基础。

Optimizing Savitzky-Golay Parameters and Its Smoothing Pretreatment for FTIR Gas Spectra

In the smoothing pretreatment for the quantitative analysis of hydrocarbon mixed gases by Fourier transform infrared analysis (FTIR),the Savitzky-Golay filter is usually used as one of the smoothing preprocessing methods in the Fourier trans-form infrared spectrum data smoothing pretreatment.However,the parameters of the Savitzky-Golay filter such as the polyno-mial order and frame size are not easy to decide.There is no one unified choice basis.Users usually adopt multiple sets in the special data set to try,and then select a set of relatively optimal data as the optimizing parameters of the Savitzky-Golay filter. The optimal selection method of the Savitzky-Golay filter parameters was explored,and the concrete calculation equations were deduced according to the relation among the normalized cut-off frequency,the normalized beginning frequency of the stopband, the normalized first side lobe peak frequency of the stopband,the normalized first side lobe peak amplitude with the polynomial order and frame size of the Savitzky-Golay filter parameters.Then when the polynomial order and frame size are set as 8 and 1 1 respectively according the above conclusion and the characteristics of the actual spectral data,the Savitzky-Golay filter smoot-hing effect is optimum.Through the acquisition the concentration of 0.1%,0.2%,0.5%,1%,2%,5% for the actual CH4 spectra,the relative maximum and minimum error of the raw spectra converted absorbance were 17.230 5% and 0.243 0% re-spectively,and the relative maximum and minimum error of the smooth spectra converted absorbance were 0.088 0% and 0.088 0% respectively in the second absorption peak.The relative error of converted absorbance was basically stable through the Savitzky-Golay filter after the spectral data preprocessing and it was relatively low,so,it laid a foundation for the late spectral data accurate qualitative and quantitative analysis.