A Framework for Circular Multilevel Systems in the Frequency Domain
In this paper, we will construct a new multilevel system in the Fourier domain using the harmonic wavelet. The main advantages of harmonic wavelet are that its frequency spectrum is confined exactly to an octave band, and its simple definition just as Haar wavelet. The constructed multilevel system...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-04-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/4/101 |
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| author | Guomin Sun Jinsong Leng Carlo Cattani |
| author_facet | Guomin Sun Jinsong Leng Carlo Cattani |
| author_sort | Guomin Sun |
| collection | DOAJ |
| description | In this paper, we will construct a new multilevel system in the Fourier domain using the harmonic wavelet. The main advantages of harmonic wavelet are that its frequency spectrum is confined exactly to an octave band, and its simple definition just as Haar wavelet. The constructed multilevel system has the circular shape, which forms a partition of the frequency domain by shifting and scaling the basic wavelet functions. To possess the circular shape, a new type of sampling grid, the circular-polar grid (CPG), is defined and also the corresponding modified Fourier transform. The CPG consists of equal space along rays, where different rays are equally angled. The main difference between the classic polar grid and CPG is the even sampling on polar coordinates. Another obvious difference is that the modified Fourier transform has a circular shape in the frequency domain while the polar transform has a square shape. The proposed sampling grid and the new defined Fourier transform constitute a completely Fourier transform system, more importantly, the harmonic wavelet based multilevel system defined on the proposed sampling grid is more suitable for the distribution of general images in the Fourier domain. |
| first_indexed | 2024-04-13T07:01:30Z |
| format | Article |
| id | doaj.art-e36a65f8e1ca46c083700481b98d815d |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-13T07:01:30Z |
| publishDate | 2018-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e36a65f8e1ca46c083700481b98d815d2022-12-22T02:57:07ZengMDPI AGSymmetry2073-89942018-04-0110410110.3390/sym10040101sym10040101A Framework for Circular Multilevel Systems in the Frequency DomainGuomin Sun0Jinsong Leng1Carlo Cattani2School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, ChinaSchool of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu 610054, ChinaEngineering School, DEIM, University of Tuscia, 01100 Viterbo, ItalyIn this paper, we will construct a new multilevel system in the Fourier domain using the harmonic wavelet. The main advantages of harmonic wavelet are that its frequency spectrum is confined exactly to an octave band, and its simple definition just as Haar wavelet. The constructed multilevel system has the circular shape, which forms a partition of the frequency domain by shifting and scaling the basic wavelet functions. To possess the circular shape, a new type of sampling grid, the circular-polar grid (CPG), is defined and also the corresponding modified Fourier transform. The CPG consists of equal space along rays, where different rays are equally angled. The main difference between the classic polar grid and CPG is the even sampling on polar coordinates. Another obvious difference is that the modified Fourier transform has a circular shape in the frequency domain while the polar transform has a square shape. The proposed sampling grid and the new defined Fourier transform constitute a completely Fourier transform system, more importantly, the harmonic wavelet based multilevel system defined on the proposed sampling grid is more suitable for the distribution of general images in the Fourier domain.http://www.mdpi.com/2073-8994/10/4/101harmonic waveletfilteringmultilevel system |
| spellingShingle | Guomin Sun Jinsong Leng Carlo Cattani A Framework for Circular Multilevel Systems in the Frequency Domain Symmetry harmonic wavelet filtering multilevel system |
| title | A Framework for Circular Multilevel Systems in the Frequency Domain |
| title_full | A Framework for Circular Multilevel Systems in the Frequency Domain |
| title_fullStr | A Framework for Circular Multilevel Systems in the Frequency Domain |
| title_full_unstemmed | A Framework for Circular Multilevel Systems in the Frequency Domain |
| title_short | A Framework for Circular Multilevel Systems in the Frequency Domain |
| title_sort | framework for circular multilevel systems in the frequency domain |
| topic | harmonic wavelet filtering multilevel system |
| url | http://www.mdpi.com/2073-8994/10/4/101 |
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