On the Design of a Class of Analog Filters Whose Impulse Response Is a Mittag‐Leffler Function

Abstract

ABSTRACT Fractional‐order filters whose impulse response is a Mittag‐Leffler (M‐L) function in any of its known forms are summarized in this work. Efficient approximation and design of these filters is then achieved through the utilization of a curve‐fitting–based method, which simultaneously minimizes the error in filter magnitude and phase. This class of filters is labeled as the “time‐domain M‐L filters,” which is different from the “frequency‐domain M‐L filters” class recently reported in the literature. In particular, the former class has an impulse response function based on M‐L kernel, whereas the latter has a transfer function based on this kernel. Simulation results using Cadence and experimental results using a field programmable analog array (FPAA) validate the introduced concept for selected cases.