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Various applications of digital signal processing, such as beamforming, data alignment, rate conversion, resampling, etc., incorporate interpolating filters to implement delays which are a certain fraction of the sampling period. This paper presents an approach to the design of equiripple IIR interpolators and compares their performance with that of previously reported FIR versions. The design approach applies the Fletcher Powell gradient technique to the optimization of an all-pass filter transfer function. The required filter processing load is seen to be considerably less than that of the FIR filter with equal phase ripple. A structure is proposed for implementing the IIR interpolators.