Periodic wavelet frames and time-frequency localization
Elena A. Lebedeva, J\"urgen Prestin
TL;DR
This paper constructs a family of Parseval periodic wavelet frames that achieve optimal time-frequency localization, improving the state of the art in multiresolution analysis.
Contribution
It introduces a new family of wavelet frames with optimal localization properties in the periodic setting, advancing the theoretical understanding of wavelet analysis.
Findings
Achieves optimal time-frequency localization according to Breitenberger uncertainty constant.
Provides the best known localization results in the context of multiresolution analysis.
Constructs a family of Parseval wavelet frames with these properties.
Abstract
A family of Parseval periodic wavelet frames is constructed. The family has optimal time-frequency localization (in the sense of the Breitenberger uncertainty constant) with respect to a family parameter and it has the best currently known localization with respect to a multiresolution analysis parameter.
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