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Matematicheskie Zametki, 2024, Volume 115, Issue 3, Pages 385–391
DOI: https://doi.org/10.4213/mzm14042 (Mi mzm14042) 		 
Approximation by Refinement Masks

E. A. Lebedeva

Saint Petersburg State University
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DOI: https://doi.org/10.4213/mzm14042
Abstract: We construct a Parseval wavelet frame with a compact support for an arbitrary continuous $2\pi$-periodic function $f$, $f(0)=1$, satisfying the inequality $|f(x)|^2+|f(x+\pi)|^2\leqslant 1$. The frame refinement mask uniformly approximates $f$. The refining function has stable integer shifts.
Keywords: refinement mask, unitary extension principle, Parseval wavelet frame, stability of integer shifts, filter bank, exact reconstruction.
Funding agency Grant number
Russian Science Foundation 23-11-00178
This work was financially supported by the Russian Science Foundation, grant no. 23-11-00178, https://rscf.ru/en/project/23-11-00178/.
Received: 24.05.2023
Revised: 29.09.2023
English version:
Mathematical Notes, 2024, Volume 115, Issue 3, Pages 352–357
DOI: https://doi.org/10.1134/S0001434624030076
Bibliographic databases:
Document Type: Article
UDC: 517
MSC: 42C40
Language: Russian
Citation: E. A. Lebedeva, “Approximation by Refinement Masks”, Mat. Zametki, 115:3 (2024), 385–391; Math. Notes, 115:3 (2024), 352–357
Citation in format AMSBIB
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\paper Approximation by Refinement Masks
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\vol 115
\issue 3
\pages 385--391
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\crossref{https://doi.org/10.4213/mzm14042}
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\transl
\jour Math. Notes
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\vol 115
\issue 3
\pages 352--357
\crossref{https://doi.org/10.1134/S0001434624030076}
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