New Optimized IIR Low-Pass Differentiators

In this paper a novel approach is proposed for approximating Parks-McClellan low-pass differentiators using optimized low-order IIR filters. Indeed, a suitable IIR filter is designed for approximating Parks- McClellan Low pass differentiator using modified Al-Alaoui´s method, and then denominator polynomial coefficients of resulting transfer function optimized by Genetic algorithm. A suitable fitness function is defined to optimize both magnitude and phase responses; moreover, appropriate weighting coefficients and GA parameters are reported for several cut-off frequencies. It is shown that the order-4 proposed low-pass differentiators yield a frequency response which is almost equal to order-30 Parks-McClellan low-pass differentiators. Furthermore, they yield steep roll-off properties, small magnitude error and almost linear phase in the pass-band; the percentage error of magnitude response is less than 0.5%.