Design of IIR Lowpass Differentiators Based on Second-Order Allpass Filter Application

The paper investigates the design of infinite-impulse response lowpass differentiators based on second-order allpass filter application. Specifications of the lowpass differentiator are first transformed into specifications of an equivalent second-order allpass filter. Unknown allpass filter coefficients are then determined such that relative passband magnitude response error of the corresponding lowpass differentiator is either minimized in the Chebyshev sense or maximally flat about some frequency in the passband. The main advantage of the proposed differentiators is their low group delay, which makes them suitable for real-time applications. Furthermore, the proposed equiripple design method exhibits fast convergence, while the maximally flat method is characterized by the simple closed-form expressions for the allpass filter coefficients values. Proposed lowpass differentiators are also compared with some of the existing infinite-impulse response lowpass differentiators.