There is an interesting observation using the first derivative to deconvolve an exponentially modified Gaussian:
The animation is here, https://terpconnect.umd.edu/~toh/spectrum/SymmetricalizationAnimation.gif
The main idea is that if we have an Exponentially Modified Gaussian (EMG) function, and we add a small fraction of first derivative to the original EMG, it results in recovering the original Gaussian while preserving the original area. The constant multiplier is the 1/time constant of the EMG. This is a very useful property.
Has anyone seen this deconvoluting property of the first derivative mentioned elsewhere in mathematical literature? An early reference from the 1960s from a Chemistry paper shows a picture a similar picture. This observation was just by chance, I am looking for a fundamental connection and if the first derivative can be used to deconvolute other types of convolutions besides the exponential ones.
Ref: J. W., and Charles N. Reilley. “De-tailing and sharpening of response peaks in gas chromatography.” Analytical Chemistry 37, (1965), 626-630.