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Tunable fractional Fourier transform implementation of electronic wave functions in atomically thin materials [PDF]
Beilstein Journal of Nanotechnology, 2018 A tunable fractional Fourier transform of the quantum wave function of electrons satisfying either the Schrödinger or the Dirac equation can be implemented in an atomically thin material by a parabolic potential distribution applied on a direction ...
Daniela Dragoman
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The fractional Clifford-Fourier transform [PDF]
Complex Analysis and Operator Theory, 2012 In this paper, a fractional version of the Clifford-Fourier transform is introduced, depending on two numerical parameters. A series expansion for the kernel of the resulting integral transform is derived.
De Bie, Hendrik, De Schepper, Nele
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Fractional Fourier Transform: Main Properties and Inequalities [PDF]
Mathematics, 2023 The fractional Fourier transform is a natural generalization of the Fourier transform. In this work, we recall the definition of the fractional Fourier transform and its relation to the conventional Fourier transform.
Mawardi Bahri +1 more
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The minimality of mean square error in chirp approximation using fractional fourier series and fractional fourier transform [PDF]
Scientific Reports, 2022 Chirps are familiar in nature, have a built-in resistance to noise and interference, and are connected to a wide range of highly oscillatory processes.
Omar T. Bafakeeh +9 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 ...
De Bie, Hendrik, De Schepper, Nele
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FRACTIONAL WAVELET TRANSFORM PHASE FOR IRIS IMAGE KEY POINTS MATCHING [PDF]
The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 2023 In this article the fractional phase congruency method for iris image key points descriptors is proposed. The fractional phase congruency is calculated using fractional wavelet transform through the fractional Fourier transform.
M. A. Protsenko, E. A. Pavelyeva
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Fractional Fourier Transform [PDF]
2001 European Control Conference (ECC), 2010 Chapter ...
Ozaktas, Haldun M. +2 more
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Quantum Weighted Fractional Fourier Transform
Mathematics, 2022 Quantum Fourier transform (QFT) is an important part of many quantum algorithms. However, there are few reports on quantum fractional Fourier transform (QFRFT).
Tieyu Zhao, Tianyu Yang, Yingying Chi
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Multiweighted-Type Fractional Fourier Transform: Unitarity
Fractal and Fractional, 2021 The definition of the discrete fractional Fourier transform (DFRFT) varies, and the multiweighted-type fractional Fourier transform (M-WFRFT) is its extended definition. It is not easy to prove its unitarity.
Tieyu Zhao, Yingying Chi
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Fractional Fourier Transform Meets Transformer Encoder
IEEE Signal Processing Letters, 2022 Utilizing signal processing tools in deep learning models has been drawing increasing attention. Fourier transform (FT), one of the most popular signal processing tools, is employed in many deep learning models. Transformer-based sequential input processing models have also started to make use of FT.
Furkan Sahinuc, Aykut Koc
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