Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9500323 | Applied and Computational Harmonic Analysis | 2005 | 8 Pages |
Abstract
The incompatibility between numerical stability and high time-frequency localization for Weyl-Heisenberg systems at critical density is formulated in the context of joint time-frequency analysis. By using the essential support and the entropy of time-frequency transforms (Windowed Fourier, Wigner and Radar-Ambiguity transform) for the description of time-frequency localization it is shown that for the class of Weyl-Heisenberg frames with given frame bounds the lower bounds on essential support and entropy both exceed the corresponding lower bounds for the class of square integrable functions. The stability-localization antagonism is expressed as a relation between the bounds on the time-frequency localization and the frame bounds describing the class of Weyl-Heisenberg frames.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Peter Korn,