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A Didactic and Visual Approach to the Fourier Transform
Revista Brasileira de Ensino de Física, 2023 This work provides a comprehensive derivation of the Fourier transform, with less emphasis on the mathematical rigor associated with the theory. Instead, its primary goal is to serve as a didactic resource that fosters an understanding of various ...
Daniel José Kmita +1 more
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Quadratic Fourier Transforms [PDF]
Annals of Functional Analysis, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Castro, L. P. +4 more
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Fractional Hartley Transform and its Inverse
مجلة بغداد للعلوم, 2023 The Hartley transform generalizes to the fractional Hartley transform (FRHT) which gives various uses in different fields of image encryption. Unfortunately, the available literature of fractional Hartley transform is unable to provide its inversion ...
Vasant Gaikwad
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Engineering Proceedings, 2023 For front-end wireless applications in small battery-powered devices, discrete Fourier transform (DFT) is a critical processing method for discrete time signals. Advanced radix structures are created to reduce the impact of transistor malfunction.
Ernest Ravindran Ramaswami Sachidanandan +2 more
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The cylindrical Fourier transform [PDF]
, 2010 In this paper we devise a so-called cylindrical Fourier transform within the Clifford analysis context. The idea is the following: for a fixed vector in the image space the level surfaces of the traditional Fourier kernel are planes perpendicular to that
A. Erdélyi +5 more
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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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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
semanticscholar +1 more source
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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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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