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A New Pseudo-Spectral Method Using the Discrete Cosine Transform

The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory a...

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Detalles Bibliográficos
Autor principal: Ito, Izumi
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2020
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8321024/
https://www.ncbi.nlm.nih.gov/pubmed/34460717
http://dx.doi.org/10.3390/jimaging6040015
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author Ito, Izumi
author_facet Ito, Izumi
author_sort Ito, Izumi
collection PubMed
description The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory approximations around both sides appear due to the periodicity resulting from the DFT. To address this problem, we propose a new PS method based on symmetric extension. We mathematically derive the proposed method using the discrete cosine transform (DCT) in the forward transform from the relation between DFT and DCT. DCT allows a sequence to function as a symmetrically extended sequence and estimates derivatives in the transformed domain. The superior performance of the proposed method is demonstrated through image interpolation. Potential applications of the proposed method are numerical simulations using the Fourier based PS method in many fields such as fluid dynamics, meteorology, and geophysics.
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spelling pubmed-83210242021-08-26 A New Pseudo-Spectral Method Using the Discrete Cosine Transform Ito, Izumi J Imaging Article The pseudo-spectral (PS) method on the basis of the Fourier transform is a numerical method for estimating derivatives. Generally, the discrete Fourier transform (DFT) is used when implementing the PS method. However, when the values on both sides of the sequences differ significantly, oscillatory approximations around both sides appear due to the periodicity resulting from the DFT. To address this problem, we propose a new PS method based on symmetric extension. We mathematically derive the proposed method using the discrete cosine transform (DCT) in the forward transform from the relation between DFT and DCT. DCT allows a sequence to function as a symmetrically extended sequence and estimates derivatives in the transformed domain. The superior performance of the proposed method is demonstrated through image interpolation. Potential applications of the proposed method are numerical simulations using the Fourier based PS method in many fields such as fluid dynamics, meteorology, and geophysics. MDPI 2020-03-28 /pmc/articles/PMC8321024/ /pubmed/34460717 http://dx.doi.org/10.3390/jimaging6040015 Text en © 2020 by the author. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) ).
spellingShingle Article
Ito, Izumi
A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title_full A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title_fullStr A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title_full_unstemmed A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title_short A New Pseudo-Spectral Method Using the Discrete Cosine Transform
title_sort new pseudo-spectral method using the discrete cosine transform
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8321024/
https://www.ncbi.nlm.nih.gov/pubmed/34460717
http://dx.doi.org/10.3390/jimaging6040015
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