Stability of iterated dyadic filter banks

TL;DR

This paper investigates the stability conditions of dyadic filter banks when iterated finitely or infinitely, establishing links between their stability properties and providing sufficient conditions for stability in specific cases.

Contribution

It offers new theoretical insights into the stability of iterated dyadic filter banks, including conditions linking finite and infinite cases and a sufficient stability criterion for certain filters.

Findings

Infinite stability guarantees finite stability with uniform bounds

Conditions are provided for finite stability implying infinite stability

A sufficient condition for stability of specific finitely supported filters

Abstract

This paper examines the frame properties of finitely and infinitely iterated dyadic filter banks. It is shown that the stability of an infinitely iterated dyadic filter bank guarantees that of any associated finitely iterated dyadic filter bank with uniform bounds. Conditions under which the stability of finitely iterated dyadic filter banks with uniform bounds implies that of the infinitely iterated dyadic filter bank are also given. The main result describes a sufficient condition under which the infinitely iterated dyadic filter bank associated with a specific class of finitely supported filters is stable.