Savitzky–Golay filter

The Savitzky- Golay filter is a mathematical smoothing filter in the signal processing. It was first described in 1964 by Abraham Savitzky and Marcel JE Golay ..

It provides substantially a polynomial regression (k -th degree ) over a series of values ​​( at least k 1 interpolation points which are treated as equidistant) to determine a smoothed value for each point. One advantage of the Savitzky -Golay filter is that which incorporates unlike other smoothing filters, shares of high frequencies are not simply cut off, but in the calculation. Thereby the filter has excellent characteristics such as the relative distribution of maxima, minima and dispersion to obtain commonly distorted by conventional methods such as the formation of the moving average by flattening or displacement.

As already mentioned, the filter uses a variable window width and variable smoothing factors; these values ​​decisively influence the effect of the filter. Thus, the filter by adjusting the coefficients not only act as a Polynomialglättung but also as a moving average or even a smoothed derivative.

The Savitzky -Golay filter is applied eg in spectroscopy. Nevertheless, the first publication of Savitzky and Golay by some authors is considered to be one of the most important and most cited basis publications in the field of computer-aided numerical analysis.