Closed-Form Orthogonal DFT Eigenvectors Generated by Complete Generalized Legendre Sequence
Closed-Form Orthogonal DFT Eigenvectors Generated by Complete Generalized Legendre Sequence
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DOI：
10.1109/tcsi.2008.925353
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发表时间：
2008-05
期刊：
影响因子：
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通讯作者：
S. Pei;Chia-Chang Wen;Jian-Jiun Ding
中科院分区：
文献类型：
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作者：
S. Pei;Chia-Chang Wen;Jian-Jiun Ding
In this paper, we propose a new method for deriving the closed-form orthogonal discrete Fourier transform (DFT) eigenvectors of arbitrary length using the complete generalized Legendre sequence (CGLS). From the eigenvectors, we then develop a novel method for computing the DFT. By taking a specific eigendecomposition to the DFT matrix, after proper arrangement, we can derive a new fast DFT algorithm with systematic construction of an arbitrary length that reduces the number of multiplications needed as compared with the existing fast algorithm. Moreover, we can also use the proposed CGLS-like DFT eigenvectors to define a new type of the discrete fractional Fourier transform, which is efficient in implementation and effective for encryption and OFDM.
