The Fractional Fourier Transform: with Applications in Optics and Signal Processing

By H. Ozaktas, M. Kutay-Alper, Z. Zalevsky. 2001

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Short-time Fourier transform: two fundamental properties and an optimal implementation (2003, methodology): “The Hermite-Gaussian functions form the complete set of eigenfunctions of the FrFT operator defined in (9) [21].”
Paley–Wiener theorems and uncertainty principles for the windowed linear canonical transform (2012, methodology): “Many operations, such as the FT, the fractional FT (FRFT) [1, 3], the Fresnel transform [9], the Lorentz transform [7], and scaling operations are its special cases.”
Fractional Fourier transforms on $L^p$ and applications (2020, background): “, [18]), optical system and optical signal processing (cf.”
Fractional Differential Mask: A Fractional Differential-Based Approach for Multiscale Texture Enhancement (2010, background): “Many ﬁndings show that fractional-based algorithms [43]–[48] are the powerful approaches for dealing with nonproblems.”
Generalized prolate spheroidal wave functions for offset linear canonical transform in Clifford analysis (2013, background): “It has recently received much attention in signal processing and optics [15, 17, 24].”
Fractional Fourier transform as a signal processing tool: An overview of recent developments (2011, methodology): “It should be mentioned that the LCT is also called the affine Fourier transform, the generalized Fresnel transform, the Collins formula, the ABCD transform, or the almost Fourier and almost Fresnel transformation [1,45].”