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2017 55th Annual Allerton Conference on Communication, Control, and Computing (Allerton), 2017 We consider the problem of computing the Fourier transform of high-dimensional vectors, distributedly over a cluster of machines consisting of a master node and multiple worker nodes, where the worker nodes can only store and process a fraction of the inputs.
Yu, Qian +2 more
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Quantum Fourier transform revisited [PDF]
Numerical Linear Algebra with Applications, 2020 SummaryThe fast Fourier transform (FFT) is one of the most successful numerical algorithms of the 20th century and has found numerous applications in many branches of computational science and engineering. The FFT algorithm can be derived from a particular matrix decomposition of the discrete Fourier transform (DFT) matrix.
Daan Camps, Roel Van Beeumen, Chao Yang
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A caveat about applications of the unilateral Fourier transform [PDF]
Revista Brasileira de Ensino de Física, 2020 It is presented a warning about the erroneous use of unilateral Fourier transform with nonhomogeneous Dirichlet or Neumann boundary conditions in a well-known textbook on integral transforms, and also in a few papers recently diffused in the literature.
Antonio S. de Castro
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Journal of Fourier Analysis and Applications, 2023 AbstractThe paper deals with the problem under which conditions for the parameters $$s_1,s_2\in \mathbb R$$ s 1 , s 2 ∈
Dorothee D. Haroske +2 more
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More on the quantum harmonic oscillator via unilateral Fourier transform [PDF]
Revista Brasileira de Ensino de Física, 2022 The stationary states of the quantum harmonic oscillator are properly determined by means of the unilateral Fourier transform without having to recourse to the properties of the confluent hypergeometric functions. This simpler procedure is reminiscent of
Douglas Willian Vieira +1 more
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Nonlinearizad of Fast Fourier Transform
Цифровые модели и решения, 2023 A unified mathematical form of reversible nonlinear transformations based on a nonlinear tensor product is presented in the form of fast algorithms.
Valeriy Labunets +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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Fourier ptychography algorithm based on scaled Fourier transform
Electronics Letters, 2021 This letter discusses an alternative Fourier ptychography algorithm based on the scaled fast Fourier transform propagation. The advantage of this scheme is that it enables a zoom‐in capability of the object spectrum and complex pupil within the synthetic
Mojde Hasanzade +3 more
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Discrete Fourier transform and permutations [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2019 It is well known that the magnitudes of the coefficients of the discrete Fourier transform (DFT) are invariant under certain operations on the input data. In this paper, the effects of rearranging the elements of an input data on its DFT are studied.
S. Hui, S.H. Żak
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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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