A New Simple Algorithm for Deriving the Winograd 9-Point FFT by Using New Identical Equations for 3 × 3 Circulant and Quasi-Circulant Matrices
The Winograd small fast Fourier transform (FFT) is a method of efficiently computing the discrete Fourier transform (DFT) for data of small block length. The equations of post-additions, constant multiplication factors, and pre-additions for the Winograd 9-point FFT are given in references [3], [5],...
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| Veröffentlicht in: | Journal of Signal Processing 2021/01/01, Vol.25(1), pp.43-51 |
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| container_title | Journal of Signal Processing |
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| creator | Takahashi, Nobuaki Takago, Daisuke Takebe, Tsuyoshi |
| description | The Winograd small fast Fourier transform (FFT) is a method of efficiently computing the discrete Fourier transform (DFT) for data of small block length. The equations of post-additions, constant multiplication factors, and pre-additions for the Winograd 9-point FFT are given in references [3], [5], [6]. A 6 × 6 block matrix is obtained from 9-point DFT matrix by matrix manipulation. By using the 6 × 6 block matrix, 3 × 3 circular and quasi-circular matrices can be derived. New identical equations for 3 × 3 circular and quasi-circular matrices have been derived by the authors. A new simple algorithm is given for the Winograd 9-point FFT correctly by using new identical equations for 3 × 3 circular and quasi-circular matrices. |
| doi_str_mv | 10.2299/jsp.25.43 |
| format | Article |
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The equations of post-additions, constant multiplication factors, and pre-additions for the Winograd 9-point FFT are given in references [3], [5], [6]. A 6 × 6 block matrix is obtained from 9-point DFT matrix by matrix manipulation. By using the 6 × 6 block matrix, 3 × 3 circular and quasi-circular matrices can be derived. New identical equations for 3 × 3 circular and quasi-circular matrices have been derived by the authors. 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The equations of post-additions, constant multiplication factors, and pre-additions for the Winograd 9-point FFT are given in references [3], [5], [6]. A 6 × 6 block matrix is obtained from 9-point DFT matrix by matrix manipulation. By using the 6 × 6 block matrix, 3 × 3 circular and quasi-circular matrices can be derived. New identical equations for 3 × 3 circular and quasi-circular matrices have been derived by the authors. A new simple algorithm is given for the Winograd 9-point FFT correctly by using new identical equations for 3 × 3 circular and quasi-circular matrices.</description><subject>Algorithms</subject><subject>circular matrix</subject><subject>Fast Fourier transformations</subject><subject>Fourier transforms</subject><subject>Mathematical analysis</subject><subject>Multiplication</subject><subject>quasi-circular matrix</subject><subject>Winograd 9-point FFT</subject><issn>1342-6230</issn><issn>1880-1013</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNpFkMtOwzAQRSMEEqWw4A8ssWKR4ldeEpuqtFCpvEQrlpbjTFpXadLaCahfwZIP4sdwCZTNzGh05o7u9bxzgnuUJsnV0q57NOhxduB1SBxjn2DCDt3MOPVDyvCxd2LtEuMwjALW8T766AHe0YterQtA_WJeGV0vViivDLoBo990OUf1AtCrLqu5kRlK_KdKlzUajaYo3aKZ3RE7jXEGZa2VLNBw08haV6X9kWHo69OVgTaqKaS7lGWGnhtptf-_u5e10QrsqXeUy8LC2W_verPRcDq48yePt-NBf-IrkmDmEwWUZs6a86Wc70gyAA4ZjwmLCaUhT9MgUDhUkGbOKw9jBjTKcZCxJOaUdb2LVndtqk0DthbLqjGleykoj3gQRoyEjrpsKWUqaw3kYm30SpqtIFjs8hYub0EDwZljr1t2aWs5hz0pjQulgD-StPh-rRbSCCjZN0fmiDM</recordid><startdate>20210101</startdate><enddate>20210101</enddate><creator>Takahashi, Nobuaki</creator><creator>Takago, Daisuke</creator><creator>Takebe, Tsuyoshi</creator><general>Research Institute of Signal Processing, Japan</general><general>Japan Science and Technology Agency</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20210101</creationdate><title>A New Simple Algorithm for Deriving the Winograd 9-Point FFT by Using New Identical Equations for 3 × 3 Circulant and Quasi-Circulant Matrices</title><author>Takahashi, Nobuaki ; Takago, Daisuke ; Takebe, Tsuyoshi</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1903-1ce22d013134c2997a3ee4ed4813812264bb55c06cebd0664683e27f05d398423</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng ; jpn</language><creationdate>2021</creationdate><topic>Algorithms</topic><topic>circular matrix</topic><topic>Fast Fourier transformations</topic><topic>Fourier transforms</topic><topic>Mathematical analysis</topic><topic>Multiplication</topic><topic>quasi-circular matrix</topic><topic>Winograd 9-point FFT</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Takahashi, Nobuaki</creatorcontrib><creatorcontrib>Takago, Daisuke</creatorcontrib><creatorcontrib>Takebe, Tsuyoshi</creatorcontrib><collection>CrossRef</collection><jtitle>Journal of Signal Processing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Takahashi, Nobuaki</au><au>Takago, Daisuke</au><au>Takebe, Tsuyoshi</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A New Simple Algorithm for Deriving the Winograd 9-Point FFT by Using New Identical Equations for 3 × 3 Circulant and Quasi-Circulant Matrices</atitle><jtitle>Journal of Signal Processing</jtitle><addtitle>Journal of Signal Processing</addtitle><date>2021-01-01</date><risdate>2021</risdate><volume>25</volume><issue>1</issue><spage>43</spage><epage>51</epage><pages>43-51</pages><issn>1342-6230</issn><eissn>1880-1013</eissn><abstract>The Winograd small fast Fourier transform (FFT) is a method of efficiently computing the discrete Fourier transform (DFT) for data of small block length. 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| source | Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals; J-STAGE (Japan Science & Technology Information Aggregator, Electronic) Freely Available Titles - Japanese |
| subjects | Algorithms circular matrix Fast Fourier transformations Fourier transforms Mathematical analysis Multiplication quasi-circular matrix Winograd 9-point FFT |
| title | A New Simple Algorithm for Deriving the Winograd 9-Point FFT by Using New Identical Equations for 3 × 3 Circulant and Quasi-Circulant Matrices |
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