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Home Bivariate Data Smoothing Savitzky-Golay Filter - Coefficients
See also: Savitzky-Golay filter, Parametric and Non-Parametric Tests 

Savitzky-Golay Filter - Coefficients

The following equation defines the general filter equation according to Savitzky and Golay. The particular behavior of the filter can be incfluenced by chosing appropriate filter coefficients. Thus one can generate both the moving average filter, the polynomial fit, and the smoothed derivatives simply by adjusting the coefficients of this equation. The parameter np defines the number of data points used for the smoothing.

Polynomial smoothing (cubic polynomials)

As the coefficients of the polynomial fit are symmetric (ai = a-i), only the positive coefficients are listed in the following table.

Smoothed first derivative

The coefficients for the calculation of the smoothed first derivative are defined by the following simple relationship:

ai = i

The standardization factors h are listed in the following table:

Smoothed second derivative

As the coefficients of the second derivative are symmetric (ai = a-i), only the positive coefficients are listed:


Home Bivariate Data Smoothing Savitzky-Golay Filter - Coefficients