Adaptive Smoothing of Spectroscopic Data by a Linear Mean-Square Estimation

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Abstract
An adaptive smoothing method based on a least mean-square estimation is developed for noise filtering of spectroscopic data. The algorithm of this method is nonrecursive and shift-varying with the local statistics of data. The mean and the variance of the observed spectrum at an individual sampled point are calculated point by point from its local mean and variance. By this method, in the resultant spectrum, the signal-to-noise ratio is maximized at any local section of the entire spectrum. Experimental results for the absorption spectrum of ammonia gas demonstrate that this method distorts less amount of signal components than the conventional smoothing method based on the polynomial curve-fitting and suppresses noise components satisfactorily. The computation time of this algorithm is rather shorter than that of the convolution algorithm with seven weighting coefficients. The a priori information for the estimation of the signal by this method are: the variance of noise, which can be attainable in the experiment; and the window function which gives the local statistics. The investigation of various types of window functions shows that the selection of the window function does not directly affect the performance of adaptive smoothing.

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