Nicolae Cotfas, Daniela Dragoman
The definition of the continuous fractional Fourier transform is based on the use of a system of eigenfunctions of the continuous Fourier transform, namely, the Hermite-Gaussian functions. A discrete fractional Fourier transform completely analogous to the continuous fractional Fourier transform can be defined by using an adequate discrete counterpart of the Hermite-Gaussian functions. The finite frame quantization is a discrete counterpart of the coherent state quantization. It is known that the quantum harmonic oscillator can be defined in terms of the coherent state quantization. By using the finite frame quantization, we obtain a discrete counterpart of the quantum harmonic oscillator. The eigenfunctions of the finite oscillator obtained in this way represent a discrete counterpart of the Hermite-Gaussian functions adequate for a new definition of the discrete fractional Fourier transform. This new definition is compared with the main existing definitions of the discrete fractional Fourier transform.
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http://arxiv.org/abs/1301.0704
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