Sharpening of Peaks and Shoulders

Another important effect if peaks with different peak-FWHM ratios are differentiated, made evident in Fig. 2-12, is that flat signals become smooth and steep signals become sharp. It can be shown that e.g. the maximal height of the inverted second derivative is proportional to the second power of the inverted ratio 

Derivative peaks of order need power of the FWHM ratio in Eq. (2-38) In this way small shoulders are strengthened, but the main signal, which is flat, disappears with higher-order differentiation (see Fig. 2-13). Signal sharpening of shoulders also becomes evident in Fig. 2-14 [33]. For further information see [33 and 36-40]. 

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