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Proceedings Paper

Topological obstructions to localization results
Author(s): Radu V. Balan
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Paper Abstract

In this paper we present topology aspects in non- localization results. A well-known such no-go result in the Balian-Low theorem that states the generator of a Weyl- Heisenberg Riesz basis cannot be well time-frequency localized. More general, the statement applies to multi WH Riesz bases, or super frames as well. These results turn out to be connected to non-triviality of a complex vector bundle. Another class of problem is related to optimality of coherent approximations of stochastic signals. More specific, for a given deficit ((alpha) (beta) >1), find the best Riesz sequence generator optimal to respect to the mean square approximation error. A topological obstruction turns out to be responsible for ill-localization of the optimal generator.

Paper Details

Date Published: 5 December 2001
PDF: 8 pages
Proc. SPIE 4478, Wavelets: Applications in Signal and Image Processing IX, (5 December 2001); doi: 10.1117/12.449701
Show Author Affiliations
Radu V. Balan, Siemens Corporate Research, Inc. (United States)

Published in SPIE Proceedings Vol. 4478:
Wavelets: Applications in Signal and Image Processing IX
Andrew F. Laine; Michael A. Unser; Akram Aldroubi, Editor(s)

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