Oversampling of wavelet frames for real dilations

TL;DR

This paper extends the Second Oversampling Theorem for wavelet frames from integer to real dilations and explores how oversampling affects shift invariance in wavelet subspaces.

Contribution

It generalizes the oversampling theorem to real dilations and analyzes the impact on shift invariance in wavelet frames.

Findings

Generalization of the Second Oversampling Theorem to real dilations

Relationship between dilation oversampling and shift invariance gain

Enhanced understanding of wavelet frame structures

Abstract

We generalize the Second Oversampling Theorem for wavelet frames and dual wavelet frames from the setting of integer dilations to real dilations. We also study the relationship between dilation matrix oversampling of semi-orthogonal Parseval wavelet frames and the additional shift invariance gain of the core subspace.