Derivatives in Spectroscopy

Derivatives often present the data in spectra in a manner that brings out the information that we are interested in, such as the number and position of bands, and their relative intensity, and removes unwanted baseline variation. Two major methods of calculating derivative spectra are the Savitzkly-Golay method of polynomial curve-fitting, and the Norris Segment-Gap method. Both of these methods can be presented as convolution processes. The definition of the Norris Derivatives is clarified by presenting the Norris Derivatives as convolution functions. A new, normalized form of Norris derivatives is derived that preserves the basic shapes of the calculated derivatives but brings the results into agreement with the Savitzky-Golay results over a range of parameters in both methods. The effectiveness of the convolution functions in removing the random high frequency noise in the spectra can be evaluated by calculating an index called RSSK/Norm, the square root of the sum of the squares of the convolution coefficients, divided by the normalization constant. he agreement and utility of the 2 methods of calculating derivatives is demonstrated by evaluating the results of using derivatives up to the fourth order on the second overtone aromatic CH band of polystyrene as an examples, in the 1680 nm region of the NIR.