Towards a single recommended optimal convolutional smoothing algorithm for electron and other spectroscopies

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Abstract
An analysis is made of the noise reduction and peak distortion arising from various methods of digital smoothing. The use of a range of convolutional smoothing algorithms and their multiple repeats, N is first considered. It is found that the width of the peak and the noise reductions arising from multiple repeats follow the expected N0.5 and N0.25 dependencies, respectively, only for convolution functions that have all their factors positive. The introduction of negative contributions weakens the dependence on N and introduces oscillations in the background until, at equal strengths of the positive and negative contributions, only severe oscillations remain. Multiple repeats of those functions with only positive factors closely approach a Gaussian function. It is shown that, of the convolutional smoothing algorithms, the traditional Savitzky-Golay methods give the best smoothing for the least distortion of a natural peak shape. These methods are as effective as the optimal Wiener filter and, in turn, may be applied by an optimal rule.