Comparison of Discrete and Continuous Wavelet Transforms

TL;DR

This paper explores the theoretical and practical connections between discrete and continuous wavelet transforms, highlighting new links via operator representations and their applications in signal processing.

Contribution

It introduces novel links between discrete and continuous wavelet transforms based on generator representation theory and discusses their application in filter bank design.

Findings

New theoretical links between wavelet transform types

Representation-based approach to filter bank design

Enhanced understanding of wavelet transform interplay

Abstract

In this paper we outline several points of view on the interplay between discrete and continuous wavelet transforms; stressing both pure and applied aspects of both. We outline some new links between the two transform technologies based on the theory of representations of generators and relations. By this we mean a finite system of generators which are represented by operators in Hilbert space. We further outline how these representations yield sub-band filter banks for signal and image processing algorithms.