The multiple-parameter fractional Fourier transform
The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M...
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| Veröffentlicht in: | Science China. Information sciences 2008-08, Vol.51 (8), p.1010-1024 |
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| creator | Lang, Jun Tao, Ran Ran, QiWen Wang, Yue |
| description | The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing. |
| doi_str_mv | 10.1007/s11432-008-0073-6 |
| format | Article |
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In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.</description><identifier>ISSN: 1009-2757</identifier><identifier>ISSN: 1674-733X</identifier><identifier>EISSN: 1862-2836</identifier><identifier>EISSN: 1869-1919</identifier><identifier>DOI: 10.1007/s11432-008-0073-6</identifier><language>eng</language><publisher>Heidelberg: SP Science in China Press</publisher><subject>Computer Science ; Fourier transforms ; Information Systems and Communication Service ; Linear operators ; Operators (mathematics) ; Parameters ; 多参数傅里叶变换 ; 多样性 ; 权重系数</subject><ispartof>Science China. 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Information sciences</title><addtitle>Sci. China Ser. F-Inf. Sci</addtitle><addtitle>Science in China(Series F)</addtitle><description>The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. 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Information sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lang, Jun</au><au>Tao, Ran</au><au>Ran, QiWen</au><au>Wang, Yue</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The multiple-parameter fractional Fourier transform</atitle><jtitle>Science China. Information sciences</jtitle><stitle>Sci. China Ser. F-Inf. Sci</stitle><addtitle>Science in China(Series F)</addtitle><date>2008-08-01</date><risdate>2008</risdate><volume>51</volume><issue>8</issue><spage>1010</spage><epage>1024</epage><pages>1010-1024</pages><issn>1009-2757</issn><issn>1674-733X</issn><eissn>1862-2836</eissn><eissn>1869-1919</eissn><abstract>The fractional Fourier transform （FRFT） has multiplicity, which is intrinsic in fractional operator. A new source for the multiplicity of the weight-type fractional Fourier transform （WFRFT） is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters m,n ∈ Z^M . Therefore a generalized fractional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform （MPFRFT）. It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.</abstract><cop>Heidelberg</cop><pub>SP Science in China Press</pub><doi>10.1007/s11432-008-0073-6</doi><tpages>15</tpages></addata></record> |
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| subjects | Computer Science Fourier transforms Information Systems and Communication Service Linear operators Operators (mathematics) Parameters 多参数傅里叶变换 多样性 权重系数 |
| title | The multiple-parameter fractional Fourier transform |
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