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A new transform, called the generalized fractional Fourier transform (gFrFT), is proposed. Originally, the eigenfunctions of the fractional Fourier transform (FrFT) are known as the Hermite Gaussian functions (HGFs). Besides, in optics, the HGFs are generalized to be the generalized Hermite Gaussian functions (gHGFs) and their adjoint functions (AgHGFs). Therefore, we can define the gFrFT by the eigenvalues...
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