Taylor Series as Wide-sense Biorthogonal Wavelet Decomposition

Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is als...

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Bibliographic Details
Published inarXiv.org
Main Authors de Oliveira, H M, Lins, R D
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.02.2015
Subjects
Computer Science - Information Theory
Mathematics - Classical Analysis and ODEs
Mathematics - Information Theory
Mathematics - Mathematical Physics
Physics - Mathematical Physics
Signal analysis
Spectrograms
Taylor series
Wavelet analysis
Wavelet transforms
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Summary:Pointwise-supported generalized wavelets are introduced, based on Dirac, doublet and further derivatives of delta. A generalized biorthogonal analysis leads to standard Taylor series and new Dual-Taylor series that may be interpreted as Laurent Schwartz distributions. A Parseval-like identity is also derived for Taylor series, showing that Taylor series support an energy theorem. New representations for signals called derivagrams are introduced, which are similar to spectrograms. This approach corroborates the impact of wavelets in modern signal analysis.
ISSN:2331-8422
DOI:10.48550/arxiv.1502.01570