H-Infinity-Optimal Fractional Delay Filters

TL;DR

This paper introduces a novel sampled-data H-infinity optimization approach for designing fractional delay filters that better restore intersample behavior beyond the Nyquist frequency, surpassing traditional methods.

Contribution

It presents a new design method using modern H-infinity optimization and provides a closed-form solution under certain conditions, improving fractional delay filter performance.

Findings

Enhanced delay accuracy beyond Nyquist frequency

Effective numerical solutions via lifted transform

Closed-form solution under specific assumptions

Abstract

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data H-infinity optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time H-infinity optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method.