Signal Reconstruction via H-infinity Sampled-Data Control Theory: Beyond the Shannon Paradigm

TL;DR

This paper introduces a novel signal reconstruction method based on sampled-data H-infinity control theory, improving upon traditional Shannon-based approaches by accounting for intersample behavior and energy distribution.

Contribution

It formulates signal reconstruction as an H-infinity optimization problem, providing stable, causal solutions that outperform existing methods in sound and image applications.

Findings

H-infinity criterion effectively models intersample behavior

Optimal solutions are guaranteed to be stable and causal

Demonstrated improvements in sound and image reconstruction

Abstract

This paper presents a new method for signal reconstruction by leveraging sampled-data control theory. We formulate the signal reconstruction problem in terms of an analog performance optimization problem using a stable discrete-time filter. The proposed H-infinity performance criterion naturally takes intersample behavior into account, reflecting the energy distributions of the signal. We present methods for computing optimal solutions which are guaranteed to be stable and causal. Detailed comparisons to alternative methods are provided. We discuss some applications in sound and image reconstruction.