Analog filters based on the Mittag-Leffler functions

We propose and study anew class of filters (named hereinafter the Mittag-Leffler filters) based on the MittagLeffler function E alpha,beta(z) in its single-parameter or double-parameter forms by transposing its argument to the frequency-domain; i.e. z = -s = -jco. A unique feature of these filters is that their impulse response is a Gaussian-like (delta-like) deformed and delayed impulse function for which we derive exact expressions using the H-Fox function. We also study the frequency response of this class of filters and obtain lower-order, realizable integer-order approximations of its transfer functions. A second-order curve-fitting approximation is then used to perform experimental results using a Field Programmable Analog Array platform to verify the theory.