Savitzky-Golay filter

A Savitzky-Golay filter is a digital filter applied to a set of digital data points to smooth the data, that is, to increase its precision without distorting the signal tendency. It does this by convolution: successive subsets of adjacent data points are fitted with a low-degree polynomial by the method of linear least squares. When the data points are equally spaced, the least-squares equations have an analytical solution in the form of a single set of convolution coefficients that can be applied to every subset, giving estimates of the smoothed signal, or of its derivatives, at the central point of each subset. The method was popularized by Abraham Savitzky and Marcel J. E. Golay, who published tables of convolution coefficients for various polynomials and subset sizes in 1964, and it has been extended to two- and three-dimensional data. Their paper is among the most widely cited in the journal Analytical Chemistry.