Savitzky-Golay Smoothing

Polynomial filtering method of Savitzky and Golay.

savgol(T, fl, forder = 4, dorder = 0)

Arguments

T

Vector of signals to be filtered.

fl

Filter length (for instance fl = 51..151), has to be odd.

forder

Filter order (2 = quadratic filter, 4 = quartic).

dorder

Derivative order (0 = smoothing, 1 = first derivative, etc.).

Details

Savitzky-Golay smoothing performs a local polynomial regression on a series of values which are treated as being equally spaced to determine the smoothed value for each point. Methods are also provided for calculating derivatives.

Value

Vector representing the smoothed time series.

References

See Numerical Recipes, 1992, Chapter 14.8, for details.

Author

Peter Riegler implemented a Matlab version in 2001. Based on this, Hans W. Borchers published an R version in 2003.

Note

For derivatives T2 has to be divided by the step size to the order
(and to be multiplied by k! — the sign appears to be wrong).

See also

RTisean::sav_gol, signal::sgolayfilt, whittaker.

Examples

# *** Sinosoid test function ***
ts <- sin(2*pi*(1:1000)/200)
t1 <- ts + rnorm(1000)/10
t2 <- savgol(t1, 51)
if (FALSE) { # \dontrun{
plot( 1:1000, t1, col = "grey")
lines(1:1000, ts, col = "blue")
lines(1:1000, t2, col = "red")} # }