Spectroscopy Part 3 - Computing the Derivative

We have noted that the largest value of the true first derivative occurs when X—iJL = a. Therefore the largest differences between two points will occur when they are varied from fi + a (or jx — cr) by some amount 8, the spacing, which we need to determine. Therefore we need to determine the largest difference of 

The second derivative is both simpler and more complicated to deal with. As we saw, the second derivative is maximum at the wavelength of the peak of the underlying absorbance curve, and we noted previously that the numerator term at that point increases 

In real samples, however, the wider the spacing the more likely it becomes that one of the points used for the derivative computation will be affected by the presence of other constituents in the sample, and the question of the optimum spacing for the derivative computation becomes dependent on the nature of the sample in which it is contained. 

The method we have used until now for estimating the derivative, simply calculating the difference between absorbance values of two data points spaced some distance apart (and dividing by that AX, of course), is probably the simplest method available. As we discussed in out previous chapter [4], however, there is a disadvantage associated with 

So the steps that Savitzky and Golay took to create their classic paper was as follows  

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