Title

Convolutional Frames and the Frame Potential

Document Type

Article

Publication Date

7-2005

Abstract

The recently introduced notion of frame potential has proven useful for the characterization of finite-dimensional tight frames. The present work represents an effort to similarly characterize finite-dimensional tight frames with additional imposed structure. In particular, it is shown that the frame potential still leads to a complete description of tight frames when restricted to the class of translation-invariant systems. It is natural to refer to such frames as convolutional because of the correspondence between translation-invariant systems and finite-dimensional filter banks. The fast algorithms associated with convolution represent one possible advantage over nonconvolutional frames in applications.
Abstract © Elsevier

Comments

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DOI

10.1016/j.acha.2005.02.005

Source Publication

Applied and Computational Harmonic Analysis

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