Discrete-time multi-scale systems

TL;DR

This paper introduces a novel multi-scale filtering framework using double convolution systems, establishes stability results, links to poly-disc function theory, and compares with existing white noise space models.

Contribution

It presents a new multi-scale filtering approach with stability proofs and theoretical connections, expanding the understanding of double convolution systems.

Findings

Proved stability theorems for multi-scale filtering systems

Connected the framework to poly-disc function theory

Compared with white noise space framework

Abstract

We introduce multi-scale filtering by the way of certain double convolution systems. We prove stability theorems for these systems and make connections with function theory in the poly-disc. Finally, we compare the framework developed here with the white noise space framework, within which a similar class of double convolution systems has been defined earlier.