Closed Form Approach for Constrained Design of nth-Order IIR Digital Differentiator

This work presents a new design method for nth-order infinite impulse response (IIR) differentiators. First, the cost function of the IIR differentiator is derived in closed form without frequency sampling. Next, a new optimization scheme is proposed to minimize the cost function under the pole radius constraint. Here, the magnitude and phase specifications are approximated simultaneously with a stability margin. Furthermore, discrete optimization for the IIR differentiator is presented for a specified word length constraint. The discrete optimization results in a stable IIR differentiator with finite word length coefficients owing to the stability margin. Finally, several design examples are demonstrated to evaluate the efficiency of the proposed method.