The Interaction between Standard Normal Variate and Derivatives

An example The spectra in Figure 1 are second derivative spectra, from samples of whole grain in a transmission instrument. For the record, the second derivative was computed using a Savitzky–Golay fi lter with a window width of 15, though this does not affect the point being made here. The spectra have lost seven points (half the window width) at each end as a consequence of the computation of the derivative. In Figure 2 we see the same spectra with SNV applied, after taking the derivative. The treatment with SNV has removed quite a bit of the variability between the spectra, variability that was probably due to different packing densities of the grain in the cell. Removing this variability is (probably) good if we want to calibrate for grain composition, it may be less of a good idea if we want to identify varieties, for example. The spectra in Figure 3 are the result of applying SNV fi rst and then computing the derivative from the SNV-treated spectra. The outcome is clearly not the same, nor should one expect it to be. SNV corrects for scatter by dividing each spectrum by its standard deviation. There is no simple relaT he subject of this column is that if you combine standard normal variate (SNV) and derivative pretreatments of spectra, it does matter in which order you apply them. Although I have probably written about this before, I was prompted to revisit the topic when I recently encountered an example where it matters quite a lot.