Smoothing

This function smoothes a numeric vector.

Usage

smooth(x, cf)

coefMA(hws)

coefWMA(hws)

coefSG(hws, k = 3L)

Arguments

x

numeric, i.e. m/z values.

cf

matrix, a coefficient matrix generated by coefMA, coefWMA or coefSG.

hws

integer(1), half window size, the resulting window reaches from (i - hws):(i + hws).

k

integer(1), set the order of the polynomial used to calculate the coefficients.

Value

smooth: A numeric of the same length as x.

coefMA: A matrix with coefficients for a simple moving average.

coefWMA: A matrix with coefficients for a weighted moving average.

coefSG: A matrix with Savitzky-Golay-Filter coefficients.

Details

For the Savitzky-Golay-Filter the hws should be smaller than FWHM of the peaks (full width at half maximum; please find details in Bromba and Ziegler 1981).

In general the hws for the (weighted) moving average (coefMA/coefWMA) has to bemuch smaller than for the Savitzky-Golay-Filter to conserve the peak shape.

Functions

• coefMA(): Simple Moving Average

  This function calculates the coefficients for a simple moving average.

• coefWMA(): Weighted Moving Average

  This function calculates the coefficients for a weighted moving average with weights depending on the distance from the center calculated as 1/2^abs(-hws:hws) with the sum of all weigths normalized to 1.

• coefSG(): Savitzky-Golay-Filter

  This function calculates the Savitzky-Golay-Coefficients. The additional argument k controls the order of the used polynomial. If k is set to zero it yield a simple moving average.

Note

The hws depends on the used method ((weighted) moving average/Savitzky-Golay).

References

A. Savitzky and M. J. Golay. 1964. Smoothing and differentiation of data by simplified least squares procedures. Analytical chemistry, 36(8), 1627-1639.

M. U. Bromba and H. Ziegler. 1981. Application hints for Savitzky-Golay digital smoothing filters. Analytical Chemistry, 53(11), 1583-1586.

Implementation based on: Steinier, J., Termonia, Y., & Deltour, J. (1972). Comments on Smoothing and differentiation of data by simplified least square procedure. Analytical Chemistry, 44(11), 1906-1909.

See also

Other noise estimation and smoothing functions: noise()

Author

Sebastian Gibb, Sigurdur Smarason (weighted moving average)

Examples

x <- c(1:10, 9:1)
plot(x, type = "b", pch = 20)
cf <- list(MovingAverage = coefMA(2),
           WeightedMovingAverage = coefWMA(2),
           SavitzkyGolay = coefSG(2))
for (i in seq_along(cf)) {
    lines(smooth(x, cf[[i]]), col = i + 1, pch = 20, type = "b")
}
legend("bottom", legend = c("x", names(cf)), pch = 20,
       col = seq_len(length(cf) + 1))