Design of First Order Differentiator With Parallel All-Pass Structure

Abstract

In this paper a new method for design of the first order differentiator is presented. The proposed differentiator consists of two parallel branches, i.e. direct path and IIR all-pass filter. The described design method allows one to obtain solution with minimum mean relative error at the desired region by controlling the ratio of phase response extremes. A small relative magnitude error, as well as a low phase error, at low frequencies is condition for good time domain behaviour. The obtained differentiator can be realized by means of only two multipliers, hence being a good choice for real time applications. The proposed solution provides a lower magnitude error than several known differentiators with similar phase error.