Savitzky filter coefficients

The filter coefficients Cj are tabulated in Table 3.1 for different filter widths. Figure 3.2, curve 3, demonstrates the effect of a Savitzky-Golay filter with a filter width of 5 points applied to the raw data. Compared to the 5-point moving-average filter, the obviously better fit can be seen. 

The Savitzky-Golay filter can also be used for derivation of signal curves. For this, appropriate filter coefficients are inserted as given in Table A.7 for the first derivative and in Table A.8 for the second derivative. 

It is tempting to write a routine such as SavGo l bad. m, to perform the Savitzky-Golay filtering, but we will show its numerical weakness. F is built up by the appropriate range of x-values and used to calculate the polynomial coefficients as a=F y( i-n i+n), see e.g. equation (4.31). 

Very popular is the Savitzky-Golay filter As the method is used in almost any chromatographic data processing software package, the basic principles will be outlined hereafter. A least squares fit with a polynomial of the required order is performed over a window length. This is achieved by using a fixed convolution function. The shape of this function depends on the order of the chosen polynomial and the window length. The coefficients b of the convolution function are calculated from ... 

Figure 4.4 Similar to the sliding polynomial smoothing (Savitzky Golay filter, the coefficients for 2nd order fit to a parabola) is the effect of Bromba Ziegler filters [Bromba and Ziegler, (1983c), coefficients fit to a triangle upper figure]. Both have bad low pass filter characteristics, as shown in the lower figure with the Fourier transforms of filters through 21 points each.

Table 3.1 Coefficients of the Savitzky-Golay filter for smoothing based on a quadratic/cubic polynomial according to Eg. (3.2). 

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