Time domain interpolation using differentiators

Abstract

This paper presents a general scheme of interpolation of a uniformly sampled signal at arbitrary time instants, which appears to be an efficient alternative to the existing multistage low-pass filtering scheme. Starting from the fact that the interpolated value can be expressed in terms of a Taylor series around the nearest sample value, suitable approximations are incorporated so that the evaluation of the interpolated value does not require any derivative higher than the second; the differentiations are then performed through FIR filtering. It is found that the method can work satisfactorily even with approximate differentiators obtained by truncating the coefficients to simple negative powers of two, thereby simplifying the multiplication operations to mere binary shifts. The error of approximation can be kept within specified limits by adding a few correction terms. The error behavior of the algorithm and its computational aspects have been investigated.