savitzkyGolay {prospectr} | R Documentation |
Savitzky-Golay smoothing and derivative of a data
matrix
, data.frame
or vector
.
savitzkyGolay(X,m,p,w,delta.wav)
X |
a numeric |
m |
differentiation order |
p |
polynomial order |
w |
window size (must be odd) |
delta.wav |
optional sampling interval |
The Savitzky-Golay algorithm fits a local polynomial regression on the signal. It requires evenly spaced data points. Mathematically, it operates simply as a weighted sum over a given window:
x_j\ast = \frac{1}{N}∑_{h=-k}^{k}{c_hx_{j+h}}
where x_j\ast is the new value, N is a normalizing coefficient, k is the gap size on each side of j and c_h are pre-computed coefficients, that depends on the chosen polynomial order and degree.
The sampling interval specified with the delta.wav
argument is used for scaling and get numerically correct
derivatives. The convolution function is written in
C++/Rcpp for faster computations.
Antoine Stevens
Savitzky, A., and Golay, M.J.E., 1964. Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627-1639.
Wentzell, P.D., and Brown, C.D., 2000. Signal processing in analytical chemistry. Encyclopedia of Analytical Chemistry, 9764-9800.
data(NIRsoil) spc <- 1/10^NIRsoil$spc # conversion to reflectance opar <- par(no.readonly = TRUE) par(mfrow=c(2,1),mar=c(4,4,2,2)) # plot of the 10 first spectra matplot(as.numeric(colnames(spc)),t(spc[1:10,]),type='l',xlab='',ylab='Reflectance') mtext('Raw spectra') sg <- savitzkyGolay(X = spc,1,3,11,delta.wav=2) matplot(as.numeric(colnames(sg)),t(sg[1:10,]),type='l',xlab='Wavelength /nm',ylab='1st derivative') mtext('1st derivative spectra') par(opar)