Fractional Delayer Utilizing Hermite Interpolation with Caratheodory Representation

Abstract

Fractional delay is indispensable for many sorts of signal processing applications and fractional delay filter (FDF) is a straightforward method to delay discrete signals. FDF based on Hermite interpolation with an analog differentiator has a low time-domain error, but a more complicated sampling module than Shannon sampling scheme. A simplified scheme, which is based on Shannon sampling and utilizing Hermite interpolation with a digital differentiator, will lead to a much higher time-domain error when the signal frequency approaches the Nyquist rate. In this letter, we propose a novel fractional delayer utilizing Hermite interpolation and Carathéodory representation. The samples of differential signal are obtained by Carathéodory representation from the samples of the original signal only. So only one sampler is required and the sampling module is simple. Simulation results for four types of signals demonstrate that the proposed method has significantly higher interpolation accuracy than Hermite interpolation with digital differentiator.