New Approach for Approximating Parks McClellan Low-Pass Differentiators

Abstract

In this paper a new approach is proposed for approximating Parks-McClellan low pass differentiators using low order IIR filters; indeed, proposed approach is a complement for Al-Alaoui's low pass differentiator design method; A suitable low-pass filter is cascaded with a wideband differentiator so that the overall transfer function yields digital IIR filter whose numerators represent linear phase FIR filter. Although the base is same as Al-Alaoui's method, the type and the order of low-pass filter and wideband differentiator is selected in such a manner that the overall transfer function yields steep roll-off properties, small magnitude error, good order reduction and almost linear phase in the pass-band. The proposed low-pass differentiators yield steeper roll-off properties and smaller magnitude error than Al-Alaoui's one; moreover, their magnitude response is very close to high order Parks-McClellan low-pass differentiators.