A Digital, Noninteger Order, Differentiator using Laguerre Orthogonal Sequences

This paper presents a novel procedure to design a digital, noninteger order, differentiator. The method is based on the Laguerre series expansion. Firstly, a discrete equivalent of the noninteger derivative Euler backward operator is given in the z-domain. Secondly, this operator is expanded into a Taylor series, which provides the data for the approximation of the Laguerre noninteger order digital derivative operator. Simulation results show the accuracy of the approximation, by measuring the frequency response for different values of the derivative noninteger order.