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Fractional Fourier Transform: Main Properties and Inequalities
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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Transactions of the American Mathematical Society, 1974 If f ( x ) f(x) and g ( x ) g(x) satisfy the equations \[ g ( x ) = d d x ∫ 0 ∞ 1 t ...
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The class of Clifford-Fourier transforms [PDF]
, 2011 Recently, there has been an increasing interest in the study of hypercomplex signals and their Fourier transforms. This paper aims to study such integral transforms from general principles, using 4 different yet equivalent definitions of the classical ...
De Bie, H., De Schepper, N., Sommen, F.
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Circuit of Quantum Fractional Fourier Transform
Fractal and Fractional, 2023 In this paper, we first use the quantum Fourier transform (QFT) and quantum phase estimation (QPE) to realize the quantum fractional Fourier transform (QFrFT).
Tieyu Zhao, Yingying Chi
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Fractional Fourier Transform [PDF]
, 2010 Chapter ...
Ozaktas, Haldun M. +2 more
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On Katugampola Fourier Transform
Journal of Mathematics, 2019 The aim of this article is to introduce a new definition for the Fourier transform. This new definition will be considered as one of the generalizations of the usual (classical) Fourier transform.
Tariq O. Salim +2 more
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Some Essential Relations for the Quaternion Quadratic-Phase Fourier Transform
Mathematics, 2023 Motivated by the fact that the quaternion Fourier transform is a powerful tool in quaternion signal analysis, here, we study the quaternion quadratic-phase Fourier transform, which is a generalized version of the quaternion Fourier transform.
Mawardi Bahri +1 more
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Fourier and Inverse Fourier Transform Model for Delayed Self-interferometry System
IEEE Photonics Journal, 2020 Understanding the effects of laser phase and frequency noise on laser interferometry is significant for evaluating the system performance. To precisely study the performance limit caused by laser frequency noise, here we propose and demonstrate a ...
Ling Zhang +8 more
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New Algorithm for Real-Valued Fourier Transform
Tikrit Journal of Engineering Sciences, 2023 This paper presents a direct algorithm for fast real discrete Fourier transform (RDFT) computing, using the discrete Fourier transform (DFT) conjugate symmetric property to reduce redundancies.
Sukaina K. Salih, Mounir T. Hamood
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Large-Scale Discrete Fourier Transform on TPUs
IEEE Access, 2021 In this work, we present two parallel algorithms for the large-scale discrete Fourier transform (DFT) on Tensor Processing Unit (TPU) clusters. The two parallel algorithms are associated with two DFT formulations: one formulation, denoted as KDFT, is ...
Tianjian Lu +4 more
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