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• W2029346323 startingPage "150" @default.
• W2029346323 abstract "The discrete equivalent of Hermite–Gaussian functions (HGFs) plays a critical role in the definition of a discrete fractional Fourier transform (DFRFT). The discrete equivalents are typically calculated through the eigendecomposition of a commutator matrix. In this study, the authors mainly focus on the fractionalisation of an odd time odd frequency discrete Fourier transform (O-ODFT) matrix. First, the authors propose a novel nearly tridiagonal matrix, which commutes with the O-ODFT matrix. It does not have multiple eigenvalues. The authors can determine a unique orthonormal eigenvector set based on block diagonalisation of a new commuting matrix. The eigenvectors of the new nearly tridiagonal matrix are shown to be O-ODFT eigenvectors, which are similar to the continuous HGFs. Then, the result of the eigendecomposition of the transform matrix is used in order to define the fractionalisation of O-ODFT (O-ODFRFT). The definition is exactly unitary, index additive and reduces to the O-ODFT for unit order. Finally, numerical examples are illustrated to demonstrate that the proposed O-ODFRFT is approximated to the continuous fractional Fourier transform." @default.
• W2029346323 created "2016-06-24" @default.
• W2029346323 creator A5004192864 @default.
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• W2029346323 date "2011-01-01" @default.
• W2029346323 modified "2023-10-14" @default.
• W2029346323 title "Fractionalisation of an odd time odd frequency DFT matrix based on the eigenvectors of a novel nearly tridiagonal commuting matrix" @default.
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• W2029346323 doi "https://doi.org/10.1049/iet-spr.2009.0288" @default.
• W2029346323 hasPublicationYear "2011" @default.
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