Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms
Discrete orthogonal transforms such as the discrete Fourier transform, discrete cosine transform, discrete Hartley transform, etc., are important tools in numerical analysis, signal processing, and statistical methods. The successful application of transform techniques relies on the existence of eff...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-05-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/8/5/509 |
| _version_ | 1798005823235948544 |
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| author | Aleksandr Cariow Janusz Papliński Dorota Majorkowska-Mech |
| author_facet | Aleksandr Cariow Janusz Papliński Dorota Majorkowska-Mech |
| author_sort | Aleksandr Cariow |
| collection | DOAJ |
| description | Discrete orthogonal transforms such as the discrete Fourier transform, discrete cosine transform, discrete Hartley transform, etc., are important tools in numerical analysis, signal processing, and statistical methods. The successful application of transform techniques relies on the existence of efficient fast algorithms for their implementation. A special place in the list of transformations is occupied by the discrete fractional Fourier transform (DFrFT). In this paper, some parallel algorithms and processing unit structures for fast DFrFT implementation are proposed. The approach is based on the resourceful factorization of DFrFT matrices. Some parallel algorithms and processing unit structures for small size DFrFTs such as <i>N</i> = 2, 3, 4, 5, 6, and 7 are presented. In each case, we describe only the most important part of the structures of the processing units, neglecting the description of the auxiliary units and the control circuits. |
| first_indexed | 2024-04-11T12:46:22Z |
| format | Article |
| id | doaj.art-5bac81bed31b431ba2c2c55b7e95120e |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-04-11T12:46:22Z |
| publishDate | 2019-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-5bac81bed31b431ba2c2c55b7e95120e2022-12-22T04:23:21ZengMDPI AGElectronics2079-92922019-05-018550910.3390/electronics8050509electronics8050509Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier TransformsAleksandr Cariow0Janusz Papliński1Dorota Majorkowska-Mech2West Pomeranian University of Technology Szczecin, Faculty of Computer Science and Information Technology, Zolnierska 49, 71-210 Szczecin, PolandWest Pomeranian University of Technology Szczecin, Faculty of Computer Science and Information Technology, Zolnierska 49, 71-210 Szczecin, PolandWest Pomeranian University of Technology Szczecin, Faculty of Computer Science and Information Technology, Zolnierska 49, 71-210 Szczecin, PolandDiscrete orthogonal transforms such as the discrete Fourier transform, discrete cosine transform, discrete Hartley transform, etc., are important tools in numerical analysis, signal processing, and statistical methods. The successful application of transform techniques relies on the existence of efficient fast algorithms for their implementation. A special place in the list of transformations is occupied by the discrete fractional Fourier transform (DFrFT). In this paper, some parallel algorithms and processing unit structures for fast DFrFT implementation are proposed. The approach is based on the resourceful factorization of DFrFT matrices. Some parallel algorithms and processing unit structures for small size DFrFTs such as <i>N</i> = 2, 3, 4, 5, 6, and 7 are presented. In each case, we describe only the most important part of the structures of the processing units, neglecting the description of the auxiliary units and the control circuits.https://www.mdpi.com/2079-9292/8/5/509discrete fractional Fourier transformVLSI-oriented algorithmsprocessing unit structure |
| spellingShingle | Aleksandr Cariow Janusz Papliński Dorota Majorkowska-Mech Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms Electronics discrete fractional Fourier transform VLSI-oriented algorithms processing unit structure |
| title | Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms |
| title_full | Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms |
| title_fullStr | Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms |
| title_full_unstemmed | Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms |
| title_short | Some Structures of Parallel VLSI-Oriented Processing Units for Implementation of Small Size Discrete Fractional Fourier Transforms |
| title_sort | some structures of parallel vlsi oriented processing units for implementation of small size discrete fractional fourier transforms |
| topic | discrete fractional Fourier transform VLSI-oriented algorithms processing unit structure |
| url | https://www.mdpi.com/2079-9292/8/5/509 |
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