%0 Journal Article
%T High order generalized permutational fractional Fourier transforms
%A Ran Qi-Wen
%A Yuan Lin
%A Tan Li-Ying
%A Ma Jing
%A Wang Qi
%A <br>冉启文
%A 袁琳
%A 谭立英
%A 马晶
%A 王骐
%J 中国物理 B
%D 2004
%I 
%X We generalize the definition of the fractional Fourier transform (FRFT) by extending the new definition proposed by Shih. The generalized FRFT, called the high order generalized permutational fractional Fourier transform (HGPFRFT), is a generalized permutational transform. It is shown to have arbitrary natural number M periodic eigenvalues not only with respect to the order of Hermite－Gaussian functions but also to the order of the transform. This HGPFRFT will be reduced to the original FRFT proposed by Namias and Liu's generalized FRFT and Shih's FRFT at the three limits with M=+∞, M=4k(k is a natural number), and M=4, respectively. Therefore the HGPFRFT introduces a comprehensive approach to Shih's FRFT and the original definition. Some important properties of HGPFRFT are discussed. Lastly the results of computer simulations and symbolic representations of the transform are provided.
%K Fourier transform
%K fractional Fourier transform
%K permutational fractional Fourier transform<br>傅立叶变换
%K 部分傅立叶变换
%K 部分置换傅立叶变换
%K Hermite-Gaussian函数
%K 量子器件
%U http://www.alljournals.cn/get_abstract_url.aspx?pcid=6E709DC38FA1D09A4B578DD0906875B5B44D4D294832BB8E&cid=47EA7CFDDEBB28E0&jid=CD8D6A6897B9334F09D8D1648C376FB4&aid=4CBCCBBBED94E29EA30C2D94C6398986&yid=D0E58B75BFD8E51C&vid=FC0714F8D2EB605D&iid=0B39A22176CE99FB&sid=4609832E4B5C797B&eid=50BBDFAC8381694B&journal_id=1009-1963&journal_name=中国物理&referenced_num=0&reference_num=22