Design of IIR Digital Differentiators Using Constrained Optimization

Abstract—A new optimization method for the design of fullband and lowpass IIR digital differentiators is proposed. In the new method, the passband phase-response error is minimized under the constraint that the maximum passband amplitude-response relative error is below a prescribed level. For lowpass IIR differen-tiators, an additional constraint is introduced to limit the average squared amplitude response in the stopband so as to minimize any high-frequency noise that may be present. Extensive experi-mental results are included, which show that the differentiators designed using the proposed method have much smaller maximum phase-response error for the same passband amplitude-response error and stopband constraints when compared with several differentiators designed using state-of-the-art competing methods. Index Terms—Digital differentiators, IIR filter design, design of filters by optimization. I