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Full Spectrum Matching Method
The First Derivative Correlation algorithm is the same as the Correlation algorithm, except that the first derivative of both the unknown and library spectra are taken before calculating the HQI. Even though the Correlation algorithm can compensate for noise and negative dips, it cannot correct for bad baselines. Normally, baseline correction pre-processing is used to attempt to "flatten" the unknown before applying the search algorithms. But sometimes it is not good enough. Like the other first derivative-based search algorithms, this attempts to remove the non-linear effects of the baseline that cannot be compensated for by the baseline pre-processing.
The algorithm is the same as the Correlation search except that the first derivative of both the library and the unknown are calculated. First the mean centering described in the "Correlation Algorithm" section is applied to the library and unknown spectra. Then their first derivatives are taken by subtracting previous points.
Where Lib0 and Unkn0 are defined to be equal to Lib1 and Unkn1, respectively. The Mask function is applied to both the unknown and the library before the mean centering is calculated to ensure that the masked points don't contribute to the final HQI. | 
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