pracma (version 1.8.8)

savgol: Savitzky-Golay Smoothing

Description

Polynomial filtering method of Savitzky and Golay.

Usage

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.).

Value

• Vector representing the smoothed time series.

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.

References

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

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)
plot( 1:1000, t1, col = "grey")
lines(1:1000, ts, col = "blue")
lines(1:1000, t2, col = "red")
# t3 <- whittaker(t1, lambda = 1600)
# lines(1:1000, t3, col = "darkgreen", lwd = 2)

#-----------------------------------------------------------------------
#   Whittacker Smoothing
#   Paul Eilers, 2002 (Matlab) and Nicholas Lewin-Koh, 2004 (R/S)
#-----------------------------------------------------------------------
whittaker <- function(y, lambda, d = 2){
#   Smoothing with a finite difference penalty
#   y:      signal to be smoothed
#   lambda: smoothing parameter (rough 50..1e4 smooth)
#   d:      order of differences in penalty (generally 2)
    require(SparseM, warn.conflicts = FALSE)
    m <- length(y)
    E <- as(m, "matrix.diag.csr")
    class(E) <- "matrix.csr"
    Dmat <- diff(E, differences = d)
    B <- E + (lambda * t(Dmat) %*% Dmat)
    z <- solve(B, y)
    return(z)
}