Data Analysis in the Shot Noise Limit Part III: An Adaptive Method for Data Smoothing

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Journal of Chemometrics

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Digital filter smoothing methods for shot-noise-limited data are addressed in this study. The preferred method is based on a Gaussian filter in which the width of the Gaussian filter function is varied depending on the estimate of the second derivative of the raw data. This filter is developed from the standpoint of maximum likelihood parameter estimation of the probability density function which describes shot-noise-limited data. The smoothing filter is tested and compared with the conventional sequential regression filter. This adaptive Gaussian smoothing filter works better than both the sequential regression and the adaptive Gaussian filter derived for normal noise. For data containing both high- and low-frequency components, the limiting step in the adaptive filter is an estimation of the smoothing interval. Methods for determining an optimum smoothing interval are discussed. With the optimized smoothing interval, the adaptive Gaussian filter works well for data sets with a wide range of varying frequency components. In particular, synthetic data typical of atomic emission spectra are used to test this smoothing filter.

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