Systematic study of elementary models of analytical signals in the form of peaks and waves

An analytical signal represented as a symmetrical peak or a corresponding integral curve (wave) was described using three elementary functions: Gaussian function, derivative of a logistic function, and Cauchy function. The shape and geometric properties of such an analytic peak were characterized by a triangular frame formed by the tangents at the inflection points and the asymptotes to peak branches. In the case of a wave, a frame formed by the tangent at the inflection point of the wave and the asymptotes to its lower and upper branches was used for the same purpose. The use of the shape of differential curves as increments for physicochemical calculations was discussed.