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光谱分析在分析化学,特别是定量分析中有越来越多用途。光谱测量过程中不可避免地存在随机噪声,会影响光谱分析结果。目前光谱预处理技术主要研究减小噪声的方法,未从理论上研究噪声对光谱的影响。本文从理论上推导随机噪声对光谱的影响公式,旨为后续光谱分析中噪声的减小和抑制奠定理论基础。论文从光谱测量所得原始信号为理论信号与随机噪声之和入手,推导了测量光谱的表达式,并将该表达式代入吸光度公式,推导出吸光度与噪声的关系。通过期望与方差的定义,推导了吸光度的期望与方差表达式。结果表明,实测吸光度是对理论吸光度的有偏估计,且实测吸光度中的噪声功率不仅与测量过程中的随机噪声功率有关,还与理论光谱有关。最后通过对多次重复测量的红外光谱与紫外光谱的分析说明了理论分析的正确性。因此,为了更加准确地估计光谱参数,降低光谱分析的最低检测门限,提高光谱分析的科学性、系统性、适用性与可信性,应在此理论分析基础上深入研究光谱预处理技术,以便将随机噪声对光谱的影响降低到最低程度。
Spectral analysis is used more and more in analytical chemistry, especially in quantitative analysis. There is inevitably random noise in the spectrum measurement, which will affect the result of spectral analysis. At present, the technology of spectral preprocessing mainly studies the method of reducing noise, and does not study the effect of noise on the spectrum theoretically. In this paper, the influence of random noise on the spectrum is deduced theoretically, which aims to lay the theoretical foundation for the reduction and suppression of noise in the subsequent spectral analysis. Starting from the sum of the theoretical signal and the random noise, the original measurement signal obtained from the spectrum measurement is deduced. The expression of measurement spectrum is deduced. The expression is substituted into the absorbance formula to deduce the relationship between absorbance and noise. By the definition of expectation and variance, the expression of expectation and variance of absorbance is deduced. The results show that the measured absorbance is a biased estimation of the theoretical absorbance, and the noise power in the measured absorbance is not only related to the random noise power in the measurement, but also to the theoretical spectrum. At last, the correctness of the theoretical analysis is demonstrated through the analysis of infrared spectra and ultraviolet spectra of repeated measurements. Therefore, in order to more accurately estimate the spectral parameters, reduce the minimum threshold of spectral analysis and improve the scientific, systematic, applicability and credibility of spectral analysis, we should further study the spectral pretreatment technology based on this theoretical analysis in order to The impact of random noise on the spectrum to a minimum.