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Representation of the Fourier Transform by Fourier Series
Journal of Mathematical Imaging and Vision, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Eigenfunctions of the Fourier Transform
Journal of Mathematical Sciences, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Flavia Lanzara, Vladimir Maz'ya
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Seventh International Symposium on Signal Processing and Its Applications, 2003. Proceedings., 2003
This paper proposes a new discrete Fourier transform algorithm using resonator H(z) = 1/(1 + z/sup -2 /). We call this algorithm the resonator Fourier transform (RFT). In the RFT, to calculate Fourier coefficients a/sub k/ and b/sub k/ of a frequency component f/sub k/, we sample an input signal x(t) by a sampling frequency f/sub s/ = 4f/sub k/ and ...
Yoshiaki Tadokoro, Kentaro Noguchi
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This paper proposes a new discrete Fourier transform algorithm using resonator H(z) = 1/(1 + z/sup -2 /). We call this algorithm the resonator Fourier transform (RFT). In the RFT, to calculate Fourier coefficients a/sub k/ and b/sub k/ of a frequency component f/sub k/, we sample an input signal x(t) by a sampling frequency f/sub s/ = 4f/sub k/ and ...
Yoshiaki Tadokoro, Kentaro Noguchi
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2018
In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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In the previous chapter, we observed a peculiar relation between the smoothness and the rapidity of vanishing at infinity of a function f, as well as its Fourier transform \(\hat {f}\). Based upon this observation, we introduce an important function space \(\mathfrak {S}\), which is invariant under the Fourier transforms. We then proceed to \(\mathfrak
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A Remark on Fourier Transforms
Mathematical Proceedings of the Cambridge Philosophical Society, 19361. Let f(x) be a complex function belonging to LP (−∞, ∞); i.e. let f(x) be measurable, and |f(x)|p integrable, over (−∞, ∞). The functionis called the Fourier transform of f(x), if the integral on the right exists, in some sense, for almost every value of y. It is well known that, if 1 ≤ p ≤ 2, the integral (1) converges in mean, with index p′ = p/(p –
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Fourier Transforms and Fourier Transforms N.M.R.
2023Gwenola Burgot, Jean-Louis Burgot
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Fractional Fourier transforms and their optical implementation II
Journal of the Optical Society of America A: Optics and Image Science, and Vision, 1993exaly