Savitsky-Golay filters

Polynomial Moving-Average (Savitsky-Golay) Filters.403... 

The most common applications of methods for handling sequential series in chemistry arise in chromatography and spectroscopy and will be emphasized in this chapter. An important aim is to smooth a chromatogram. A number of methods have been developed here such as the Savitsky-Golay filter (Section 3.3.1.2). A problem is that if a chromatogram is smoothed too much the peaks become blurred and lose resolution, negating the benefits, so optimal filters have been developed that remove noise without broadening peaks excessively. 

Savitsky-Golay Filters, Hanning and Hamming Windows... 

The calculation of moving average and Savitsky-Golay filters is illustrated in Table 3.4. 

Figure 3.8(a) is a representation of the raw data. The result of using MA filters is shown in Figure 3.8(b). A three point MA preserves the resolution (just), but a five point MA loses this and the cluster appears to be composed of only one peak. In contrast, the five and seven point quadratic/cubic Savitsky-Golay filters [Figure 3.8(c)] preserve resolution whilst reducing noise and only starts to lose resolution when using a nine point function. 

Smooth the data in the following five ways (a) five point moving average (b) seven point moving average (c) five point quadratic Savitsky-Golay filter (d) seven point... 

Figure 2 (A) Raw data together with the results of (B) moving average and (C) Savitsky-Golay filters.

Table 2 Savitsky-Golay filters for calculation of derivatives ...

Bromba, M.U.A., Application hints for Savitsky-Golay digital smoothing filters, Anal. Chem., 53, 1583, 1981. 

The first point of the seven point Savitsky-Golay quadratic/cubic filtered data can be calculated as follows ... 

This procedure is equivalent to the Savitsky-Golay method, algorithms for which have been included in computer software for scientific instruments such as the Fourier-transform infrared (FTIR) spectrometer. Alternatives to smoothing are weighted least-squares fitting or optimal (Weiner) filtering techniques. ... 

A. Savitsky and M. Golay, Smoothing and Filtering Functions for Analytical Data, Anal. Chem., 1964, 36, 1627-1632. 

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