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Quantum Weighted Fractional-Order Transform
Fractal and Fractional, 2023 Quantum Fourier transform (QFT) transformation plays a very important role in the design of many quantum algorithms. Fractional Fourier transform (FRFT), as an extension of the Fourier transform, is particularly important due to the design of its quantum
Tieyu Zhao, Yingying Chi
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Fractal and Fractional, 2022 In this paper, we establish two approximation theorems for the multidimensional fractional Fourier transform via appropriate convolutions. As applications, we study the boundary and initial problems of the Laplace and heat equations with chirp functions.
Yinuo Yang +3 more
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The Fractional Fourier Transform and Harmonic Oscillation [PDF]
Nonlinear Dynamics, 2002 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kutay M.A., Ozaktas H.M.
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Random fractional Fourier transform : stochastic perturbations along the axis of propagation [PDF]
, 1999 The fractional Fourier transform (FRT) is known to be optically implementable with use of a medium with a perfect radial quadratic-index profile. Using the quantum-mechanical operator formalism, we examine the effects on the FRT action of such a medium
Abe, Sumiyoshi, Sheridan, John T.
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Enhanced monopulse radar tracking using fractional Fourier filtering in the presence of interference [PDF]
, 2010 Monopulse radars are used to track a target that appears in the look direction beam width. Significant distortion is produced when manmade high power interference (jamming) is introduced to the radar processor through the radar antenna main lobe (main ...
Elgamel, Sherif A.E.H., Soraghan, J.J.
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A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for Fourier transform [PDF]
, 2004 A reverse of the Cauchy-Bunyakovsky-Schwarz integral inequality for complex-valued functions and applications for the finite Fourier transform are ...
Hanna, George T +5 more
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Using EMD-FrFT filtering to mitigate high power interference in chirp tracking radars [PDF]
, 2011 This letter presents a new signal processing subsystem for conventional monopulse tracking radars that offers an improved solution to the problem of dealing with manmade high power interference (jamming).
Soraghan, John, Elgamel, Sherif
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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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Self Fourier functions and fractional Fourier transforms [PDF]
Optics Communications, 1993 The Fourier transform is perhaps the most important analytical tool in wave optics. Hence Fourier-related concepts are likely to have an important on optics. We will likely recall two novel concepts and then show how they are interrelated. A self-Fourier function (SFF) [1,2] is a function whose Fourier transform is identical to itself.
Mendlovic, D. +2 more
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Fractional Fourier transforms of hypercomplex signals [PDF]
Signal, Image and Video Processing, 2012 An overview is given to a new approach for obtaining generalized Fourier transforms in the context of hypercomplex analysis (or Clifford analysis). These transforms are applicable to higher-dimensional signals with several components and are different from the classical Fourier transform in that they mix the components of the signal.
Hendrik De Bie, Nele De Schepper
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