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Implementation of quantum and classical discrete fractional Fourier transforms [PDF]
Nature Communications, 2016 Fourier analysis has become a standard tool in contemporary science. Here, Weimann et al. report classical and quantum optical realizations of the discrete fractional Fourier transform, a generalization of the Fourier transform, with potential ...
Steffen Weimann +11 more
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Quantum‐Inspired Fourier Transforms Based on Circuits [PDF]
Advanced ScienceFourier transform (FT) is ubiquitous in modern society due to their broad applications in many branches of science and engineering. Improving the speed of FT is a common interest in the fields of signal processing. The quantum FT is generally believed to
Hanxu Zhang, Yifan Sun, Xiangdong Zhang
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Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates [PDF]
MethodsX, 2015 The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions ...
Edem Dovlo, Natalie Baddour
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Quadratic Fourier Transforms [PDF]
Annals of Functional Analysis, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
L. P. Castro +4 more
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FNet: Mixing Tokens with Fourier Transforms [PDF]
North American Chapter of the Association for Computational Linguistics, 2021 We show that Transformer encoder architectures can be sped up, with limited accuracy costs, by replacing the self-attention sublayers with simple linear transformations that “mix” input tokens. Most surprisingly, we find that replacing the self-attention
J. Lee-Thorp +3 more
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New iterative technique for computing Fourier transforms. [PDF]
مجلة جامعة الانبار للعلوم الصرفة, 2023 The Fourier transformations have stimulated many amounts of articles in recent years. they arise in the fields of engineering, control systems, and technology like analyzing signals in electronic circuits, radio circuits, cell phones, image processing ...
Ahmad Issa, Murat Düz
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New many-parameter Fourier–Clifford transforms
Цифровые модели и решения, 2023 The article shows how ordinary complex-valued Fourier transforms are extended to Cliffordean-valued many-parameter Fourier transforms (MPFCTs). Each MPFCT depends on finite set of independent parameters (angles), which could be changed independently one ...
V. G. Labunets +2 more
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Arbitrary optical wave evolution with Fourier transforms and phase masks. [PDF]
Optics Express, 2019 A large number of applications in classical and quantum photonics require the capability of implementing arbitrary linear unitary transformations on a set of optical modes. In a seminal work by Reck et al. [Phys. Rev.
Víctor López Pastor +2 more
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Irregularity-Aware Graph Fourier Transforms [PDF]
IEEE Transactions on Signal Processing, 2018 In this paper, we present a novel generalization of the graph Fourier transform (GFT). Our approach is based on separately considering the definitions of signal energy and signal variation, leading to several possible orthonormal GFTs.
Benjamin Girault +2 more
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Approximate Fast Graph Fourier Transforms via Multilayer Sparse Approximations [PDF]
IEEE Transactions on Signal and Information Processing over Networks, 2016 The fast Fourier transform is an algorithm of paramount importance in signal processing as it allows to apply the Fourier transform in $\mathcal {O}(n \log n)$ instead of $\mathcal {O}(n^2)$ arithmetic operations.
Luc Le Magoarou +2 more
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