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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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Formato: | Online Artículo Texto |
Lenguaje: | English |
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MDPI
2020
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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. |
format | Online Article Text |
id | pubmed-8321024 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
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 |
work_keys_str_mv | AT itoizumi anewpseudospectralmethodusingthediscretecosinetransform AT itoizumi newpseudospectralmethodusingthediscretecosinetransform |