## Smoothing and derivatives

Savitzky-Golay filter is used to smooth signals and calculate derivatives. The filter has three arguments: a width of the filter (`width`

), a polynomial order (`porder`

) and the derivative order (`dorder`

). If the derivative order is zero (default value) only smoothing will be performed.

The next chunk of code takes the spectra from *Simdata*, adds additional random noise using random numbers generator for normal distribution and then applies the SG filter with different settings. The results are shown as plots under the chunk.

```
# load UV/Vis spectra from Simdata
data(simdata)
= simdata$spectra.c
ospectra attr(ospectra, "xaxis.values") = simdata$wavelength
attr(ospectra, "xaxis.name") = "Wavelength, nm"
# add random noise to the spectra
= ospectra + 0.025 * matrix(rnorm(length(ospectra)), dim(ospectra))
nspectra
# apply SG filter for smoothing
= prep.savgol(nspectra, width = 15, porder = 1)
pspectra
# apply SG filter for smoothing and take a first derivative
= prep.savgol(nspectra, width = 15, porder = 1, dorder = 1)
dpspectra
# show results
par(mfrow = c(2, 2))
mdaplot(ospectra, type = "l", main = "Original")
mdaplot(nspectra, type = "l", main = "Noise added")
mdaplot(pspectra, type = "l", main = "Smoothing")
mdaplot(dpspectra, type = "l",main = "First derivative")
```

Starting from *v.0.12.0* the algorithm has been modified in order to treat the end points better (for example, when a derivative is taken the end points may look a bit weird and have to be truncated). The implemented algorithm is based on the method described in this article.