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Accuracy of the Discrete Fourier Transform and the Fast Fourier Transform
SIAM Journal on Scientific Computing, 1996Accuracy of the discrete Fourier transform (DFT) and the fast Fourier transform (FFT) depends on the accuracy of the twiddle factors entirely. For accurate twiddle factor tables, this paper recommends to compute the sine/cosine functions with high precision arithmetic along the algorithms in terms of faster converging approximations, such as rational ...
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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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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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IEEE Transactions on Computers, 1983
This paper surveys nine designs for VLSI circuits that compute N-element Fourier transforms. The largest of the designs requires O(N2 log N) units of silicon area; it can start a new Fourier transform every O(log N) time units. The smallest designs have about 1/Nth of this throughput, but they require only 1/Nth as much area.
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This paper surveys nine designs for VLSI circuits that compute N-element Fourier transforms. The largest of the designs requires O(N2 log N) units of silicon area; it can start a new Fourier transform every O(log N) time units. The smallest designs have about 1/Nth of this throughput, but they require only 1/Nth as much area.
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Optics Letters, 1995
We propose a new method based on the differential absorption lidar technique for multipollutant detection. A broadband laser is sent into the atmosphere in a wavelength range in which several pollutants absorb. The backscattered light is analyzed by a Fourier-transform spectrometer with time resolution.
M, Douard +6 more
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We propose a new method based on the differential absorption lidar technique for multipollutant detection. A broadband laser is sent into the atmosphere in a wavelength range in which several pollutants absorb. The backscattered light is analyzed by a Fourier-transform spectrometer with time resolution.
M, Douard +6 more
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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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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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Concept, implementations and applications of Fourier ptychography
Nature Reviews Physics, 2021Guoan Zheng, Cheng Shen, Shaowei Jiang
exaly
Integrated photodetectors for compact Fourier-transform waveguide spectrometers
Nature Photonics, 2022Matthias J Grotevent, Sergii V Yakunin
exaly