H-infinity Design of Periodically Nonuniform Interpolation and Decimation for Non-Band-Limited Signals

TL;DR

This paper introduces a novel sampled-data H-infinity optimization approach for nonuniform signal interpolation and decimation, removing the need for band-limiting assumptions and enabling real-valued optimal filters.

Contribution

It proposes a new H-infinity based method for nonuniform interpolation and decimation that does not rely on band-limited signals and produces real-valued filters.

Findings

The method removes the band-limiting assumption.

Optimal filters can be real-valued.

Effectiveness demonstrated through examples.

Abstract

In this paper, we consider signal interpolation of discrete-time signals which are decimated nonuniformly. A conventional interpolation method is based on the sampling theorem, and the resulting system consists of an ideal filter with complex-valued coefficients. While the conventional method assumes band limitation of signals, we propose a new method by sampled-data H-infinity optimization. By this method, we can remove the band-limiting assumption and the optimal filter can be with real-valued coefficients. Moreover, we show that without band-limited assumption, there can be the optimal decimation patterns among ones with the same ratio. By examples, we show the effectiveness of our method.