Designing linear-phase digital differentiators a novel approach

In this paper two methods of designing efficiently a digital linear-phase differentiator of an arbitrary degree of differentiation are proposed. The first one utilizes a symbolic expression for the coefficients of a generic fractional delay filter and is based on a fundamental relationship between the coefficients of a digital differentiator and the coefficients of the generic FD filter. The second profits from one of the crucial attributes of the structure invented by Farrow for FD filters. It lies in an alternate symmetry and anti-symmetry of sub-filters which are linear-phase differentiators. The proposed design methods are illustrated by examples. Some practical remarks concerning the usage of the Farrow structure are also included.