Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500286 | Applied and Computational Harmonic Analysis | 2005 | 15 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Matthew Fickus, Brody D. Johnson, Keri Kornelson, Kasso A. Okoudjou,