Discrete Fractional Fourier Transforms Based on Closed-Form Hermite–Gaussian-Like DFT Eigenvectors | IEEE Journals & Magazine | IEEE Xplore

Discrete Fractional Fourier Transforms Based on Closed-Form Hermite–Gaussian-Like DFT Eigenvectors


Abstract:

In this paper, we construct discrete fractional Fourier transforms (DFrFT) using recently introduced closed-form Hermite-Gaussian-like (HGL) eigenvectors. With respect to...Show More

Abstract:

In this paper, we construct discrete fractional Fourier transforms (DFrFT) using recently introduced closed-form Hermite-Gaussian-like (HGL) eigenvectors. With respect to such eigenvectors, we discuss the convergence of their components to samples of the corresponding continuous Hermite-Gaussian functions and propose solutions to deal with some restrictions related to their construction. This allows us to give new procedures for obtaining orthonormal bases of HGL eigenvectors, which are used to fractionalize the discrete Fourier transform. We illustrate the application of the resulting DFrFT in the scenario of filtering in the fractional domain and compare the results with existing DFrFT approaches.
Published in: IEEE Transactions on Signal Processing ( Volume: 65, Issue: 23, 01 December 2017)
Page(s): 6171 - 6184
Date of Publication: 07 September 2017

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