High order generalized permutational fractional Fourier transforms
High order generalized permutational fractional Fourier transforms
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DOI：
10.1088/1009-1963/13/2/010
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发表时间：
2004-02
期刊：
影响因子：
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通讯作者：
Qi-Wen Ran;Yuan Lin;Li-ying Tan;Ma Jing;Wang Qi
中科院分区：
文献类型：
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作者：
Qi-Wen Ran;Yuan Lin;Li-ying Tan;Ma Jing;Wang Qi
本文推广了Shih提出的分数阶傅里叶变换的定义。广义分数阶傅里叶变换，又称高阶广义置换分数阶傅里叶变换（HGPFRFT），是一种广义置换变换。它被证明有任意的自然数M周期特征值，不仅相对于厄米高斯函数的顺序，而且顺序的变换。在M = +∞，M = 4k（k为自然数）和M = 4的三个极限下，该HGPFRFT将退化为Namias和Liu的广义FRFT和Shih的FRFT.因此，HGPFRFT介绍了一个全面的方法，施的FRFT和原始定义。讨论了HGPFRFT的一些重要性质。最后给出了计算机模拟结果和变换的符号表示。
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.