Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters

Nira Dyn; Ognyan Kounchev; David Levin; Hermann Render

doi:10.1016/j.acha.2013.12.003

Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters

Nira Dyn, Ognyan Kounchev^*, David Levin, Hermann Render

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials with real-valued parameters. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers and Dubuc. The main result is the existence and smoothness of these Daubechies type wavelets.

Original language	English
Pages (from-to)	288-306
Number of pages	19
Journal	Applied and Computational Harmonic Analysis
Volume	37
Issue number	2
DOIs	https://doi.org/10.1016/j.acha.2013.12.003
State	Published - Sep 2014

Keywords

Daubechies wavelets
Non-stationary subdivision
Non-stationary wavelets
Wavelet analysis

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10.1016/j.acha.2013.12.003

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title = "Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters",

abstract = "We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials with real-valued parameters. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers and Dubuc. The main result is the existence and smoothness of these Daubechies type wavelets.",

keywords = "Daubechies wavelets, Non-stationary subdivision, Non-stationary wavelets, Wavelet analysis",

author = "Nira Dyn and Ognyan Kounchev and David Levin and Hermann Render",

note = "Funding Information: The second named author was sponsored partially by the Alexander von Humboldt Foundation and by the Tel-Aviv University , and the second and fourth named authors were sponsored partially by Project DO-2-275/2008 “Astroinformatics” with Bulgarian NSF . ",

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doi = "10.1016/j.acha.2013.12.003",

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AU - Dyn, Nira

AU - Kounchev, Ognyan

AU - Levin, David

AU - Render, Hermann

N1 - Funding Information: The second named author was sponsored partially by the Alexander von Humboldt Foundation and by the Tel-Aviv University , and the second and fourth named authors were sponsored partially by Project DO-2-275/2008 “Astroinformatics” with Bulgarian NSF .

PY - 2014/9

Y1 - 2014/9

N2 - We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials with real-valued parameters. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers and Dubuc. The main result is the existence and smoothness of these Daubechies type wavelets.

AB - We investigate non-stationary orthogonal wavelets based on a non-stationary interpolatory subdivision scheme reproducing a given set of exponentials with real-valued parameters. The construction is analogous to the construction of Daubechies wavelets using the subdivision scheme of Deslauriers and Dubuc. The main result is the existence and smoothness of these Daubechies type wavelets.

KW - Daubechies wavelets

KW - Non-stationary subdivision

KW - Non-stationary wavelets

KW - Wavelet analysis

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SN - 1063-5203

VL - 37

SP - 288

EP - 306

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

IS - 2

ER -

Regularity of generalized Daubechies wavelets reproducing exponential polynomials with real-valued parameters

Abstract

Keywords

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