Fractional derivative of logarithmic function and its applications as multipurpose ASP circuit

Abstract

This paper presents a new approach to approximate the fractional order derivative of a logarithmic function using the Caputo definition. Further, this approximated fractional derivative has been used to conceptualize and design a multipurpose ASP (analog signal processing) circuit, by cascading the logarithmic amplifier with fractional order differentiator. The proposed multipurpose ASP circuit is capable to generate different kinds of signals (such as step signals with controlled amplitude, tangent and cotangent signals with controllable fractional power) for different inputs. Moreover, this circuit is also helpful to develop reciprocal, square root, cube root and nth-root of the input signal, up to some extent. Several types of input signals have been taken into consideration and the corresponding output responses are obtained by varying the order of differentiation in fractional sense. Numerical as-well-as circuit simulations have been done in MATLAB and PSpice environments to validate the theoretically obtained results. Further, hardware implantation has also been done to see the practical aspects of the proposed design.