Frames adapted to a phase-space cover

TL;DR

This paper introduces a method to construct frames tailored to irregular phase-space covers, optimizing their concentration in specific regions for applications in time-frequency, wavelet, and Gabor analysis.

Contribution

It provides a novel framework for creating adaptable frames aligned with arbitrary phase-space covers, enhancing analysis flexibility.

Findings

Frames are effectively adapted to irregular phase-space covers.

Applications demonstrate improved analysis in time-frequency, wavelet, and Gabor contexts.

Maximizing concentration leads to more precise localized analysis.

Abstract

We construct frames adapted to a given cover of the time-frequency or time-scale plane. The main feature is that we allow for quite general and possibly irregular covers. The frame members are obtained by maximizing their concentration in the respective regions of phase-space. We present applications in time-frequency, wavelet and Gabor analysis.