An approximating interpolation formula for bandlimited signals in the linear canonical transform domain associated with finite nonuniformly spaced samples

Abstract

In the past literature, with the reproducing property of the reproducing kernel, Zhao et al. proposed an interpolation formula for bandlimited signals in the linear canonical transform (LCT) domain associated with finite set of irregularly spaced samples. Although the authors have discussed the reconstruction error of the formula, they did not investigate the conditions that lead to the error tends to zero when the number of samples runs to infinity, i.e., the approximating property of the formula. In this paper, we firstly present a sufficient condition achieving that property with respect to Zhao's formula. Then, under a similar condition we formulate an approximating interpolation formula for bandlimited signals in the LCT domain with parameter matrix A=(a, b;c, d) associated with finite nonuniform samples of the signals’ LCT with parameter matrix A¯=(−b,a;−d,c). We also provide some potential applications of the derived reconstruction formula to show the advantage of the theory.