The discrete fractional Fourier transform

Candan, Çağatay
We propose and consolidate a definition of the discrete fractional Fourier transform that generalizes the discrete Fourier transform (DFT) in the same sense that the continuous fractional Fourier transform generalizes the continuous ordinary Fourier transform. This definition is based on a particular set of eigenvectors of the DFT matrix, which constitutes the discrete counterpart of the set of Hermite-Gaussian functions. The definition is exactly unitary, index additive, and reduces to the DFT for unit order. The fact that this definition satisfies all the desirable properties expected of the discrete fractional Fourier transform supports our confidence that it will be accepted as the definitive definition of this transform.


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Taşeli, Hasan (Springer Science and Business Media LLC, 2005-10)
Computational efficiencies of the discrete (pseudospectral, collocation) and continuous (spectral, Rayleigh-Ritz, Galerkin) variable representations of the scaled Hermite-Weber basis in finding the energy eigenvalues of Schrodinger operators with several potential functions have been compared. It is well known that the so-called differentiation matrices are neither skew-symmetric nor symmetric in a pseudospectral formulation of a differential equation, unlike their Rayleigh-Ritz counterparts. In spite of th...
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The fuzzy supersphere S-F((2,2)) is a finite-dimensional matrix approximation to the supersphere S-(2,S-2) incorporating supersymmetry exactly. Here the star-product of functions on S-F((2,2)) is obtained by utilizing the OSp(2,1) coherent states. We check its graded commutative limit to S-(2,S-2) and extend it to fuzzy versions of sections of bundles using the methods of [1]. A brief discussion of the geometric structure of our star-product completes our work.
Citation Formats
Ç. Candan and H. OZAKTAS, “The discrete fractional Fourier transform,” IEEE TRANSACTIONS ON SIGNAL PROCESSING, pp. 1329–1337, 2000, Accessed: 00, 2020. [Online]. Available: