SGFDESIGN Function

Designs a finite impulse response (FIR) Savitsky-Golay filter.

Usage

result = SGFDESIGN(m, l)

Input Parameters

m—The length of the filter.

l—The number of moments preserved by the filter.

Returned Value

result—A filter structure containing the coefficients of the FIR filter.

Keywords

None.

Discussion

SGFDESIGN designs optimal linear phase FIR filters for estimating the signal s(n) from the noise-corrupted observation

x(n) = s(n) + e(n)

where noise e(n) is an independent, identically distributed random variable.

The coefficients of the FIR filter:

 

are chosen so that the signal estimate:

 

satisfies two properties. First, the filter minimizes the error:

E[b_n*e(n)]²

where the operation E  denotes the mathematical expectation. Second, the moments of the signal s(n) are conserved up to a desired order L.

The moment constraints can be equivalently stated as requiring the filter coefficients b_n to satisfy:

 

and:

,    l = 1, 2, ..., L

This filter is most often used in the physical sciences for smoothing experimental data.

Example

This example illustrates the design of a Savitzky-Golay filter. The results are shown in Magnitude Response of Savitzky-Golay Filter.

h = SGFDESIGN(15, 4)

hf = FREQRESP_Z(h, Outfreq = f)

PLOT, f, ABS(hf), Title = 'Savitzky-Golay Filter Magnitude', $
XTitle = 'Frequency'

Magnitude Response of Savitzky-Golay Filter

For Additional Information

Schussler and Steffen, 1988, Section 8.3.2, pp. 441-443.

Savitsky and Golay, 1964. Steiner, Termonia and Deltour, 1972.