Improved discrete fractional Fourier transform [PDF]
Optics Letters, 1997 The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT's) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT.
S C, Pei, M H, Yeh
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On the class of uncertainty inequalities for the coupled fractional Fourier transform
Journal of Inequalities and Applications, 2022 The coupled fractional Fourier transform F α , β $\mathcal {F}_{\alpha ,\beta}$ is a two-dimensional fractional Fourier transform depending on two angles α and β, which are coupled in such a way that the transform parameters are γ = ( α + β ) / 2 $\gamma
Firdous A. Shah +3 more
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Novel Fractional Wavelet Transform with Closed-Form Expression [PDF]
, 2014 yesA new wavelet transform (WT) is introduced based on the fractional properties of the traditional Fourier transform. The new wavelet follows from the fractional Fourier order which uniquely identifies the representation of an input function in a ...
Abd-Alhameed, Raed A. +4 more
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Nonseparable two-dimensional fractional Fourier transform [PDF]
Applied Optics, 1998 Previous generalizations of the fractional Fourier transform to two dimensions assumed separable kernels. We present a nonseparable definition for the two-dimensional fractional Fourier transform that includes the separable definition as a special case. Its digital and optical implementations are presented.
Sahin, A., Kutay, M. A., Ozaktas, H. M.
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Uniqueness results for the phase retrieval problem of fractional Fourier transforms of variable order [PDF]
, 2010 In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics.
Jaming, Philippe
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Repeated fractional Fourier domain filtering is equivalent to repeated time and frequency domain filtering [PDF]
, 1996 Cataloged from PDF version of article.Any system consisting of a sequence of multiplicative filters inserted between several fractional Fourier transform stages, is equivalent to a system composed of an appropriately chosen sequence of multiplicative ...
Ozaktas, H. M.
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Discrete Quadratic-Phase Fourier Transform: Theory and Convolution Structures
Entropy, 2022 The discrete Fourier transform is considered as one of the most powerful tools in digital signal processing, which enable us to find the spectrum of finite-duration signals.
Hari M. Srivastava +3 more
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Anamorphic Fractional Fourier Transforming--Optical Implementation and Applications [PDF]
, 1995 Cataloged from PDF version of article.An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed.
Bitran, Y. +5 more
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Enhanced monopulse radar tracking using optimum fractional Fourier transform [PDF]
, 2010 Conventional monopulse radar processors are used to track a target that appears in the look direction beam width. The distortion produced when additional targets appear in the look direction beam width can cause severe erroneous outcomes from the ...
Elgamel, S. A., Soraghan, J.
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Parseval Relationship of Samples in the Fractional Fourier Transform Domain
Journal of Applied Mathematics, 2012 This paper investigates the Parseval relationship of samples associated with the fractional Fourier transform. Firstly, the Parseval relationship for uniform samples of band-limited signal is obtained.
Bing-Zhao Li, Tian-Zhou Xu
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