A new discrete fractional Fourier transform based on constrained eigendecomposition of DFT matrix by Largrange multiplier method
Journal
IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing
Journal Volume
46
Journal Issue
9
Pages
1240-1245
Date Issued
1999
Author(s)
Abstract
This paper is concerned with the definition of the discrete fractional Fourier transform (DFRFT). First, an eigendecomposition of the discrete Fourier transform (DFT) matrix is derived by sampling the Hermite Gauss functions, which are eigenfunctions of the continuous Fourier transform and by performing a novel error-removal procedure. Then, the result of the eigendecomposition of the DFT matrix is used to define a new DFRFT. Finally, several numerical examples are illustrated to demonstrate that the proposed DFRFT is a better approximation to the continuous fractional Fourier transform than the conventional defined DFRFT.
Type
journal article
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