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Quantum-inspired workflow for processing distributed fiber-optic sensor data. [PDF]
Sci RepGemeinhardt H, Sharma J, Kastoryano M.
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On Fourier Series on the Torus and Fourier Transforms
Mathematical Notes, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Fourier transform and the discrete Fourier transform
Inverse Problems, 1989This paper gives an error bound in computing the Fourier transform for a square summable function by means of the discrete Fourier transform. In detail description, the error bound depends on the number of samples, the interval where the samples are taken, the interval where the Fourier transform is being approximated, the local averaging in the time ...
Auslander, Louis, Grünbaum, F. Alberto
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Scientific American, 1989
To calculate a transform, just listen. The ear automatically performs the calculation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure traveling through time and the atmosphere-into a spectrum, a description of the sound as a series of volumes at ...
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To calculate a transform, just listen. The ear automatically performs the calculation, which the intellect can execute only after years of mathematical education. The ear formulates a transform by converting sound-the waves of pressure traveling through time and the atmosphere-into a spectrum, a description of the sound as a series of volumes at ...
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On Fourier-Stieltjes Transforms
Canadian Journal of Mathematics, 1955Let be the class of bounded non-decreasing functions defined on the real line which are normalized by the conditions ϕ(− ∞) = 0 , ϕ(t + 0) = ϕ(t).Let be the class of Fourier-Stieltjes transforms of elements of i.e. the elements of and are connected by the relationwhere ϕ ∊ and Φ ∊ .It is well known, and easy to verify that this mapping from to ...
Calderón, Alberto P., Devinatz, A.
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ICASSP-88., International Conference on Acoustics, Speech, and Signal Processing, 2003
A novel approach to the definition of the roots of unity in the RNS (residue number system) is presented. The definition is based on a suitable polar representation of the complex residues. The resulting RNS Fourier transform provides an algorithm for performing circular convolutions characterized by flexibility in terms of length, computational cost ...
Pietro Burrascano +4 more
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A novel approach to the definition of the roots of unity in the RNS (residue number system) is presented. The definition is based on a suitable polar representation of the complex residues. The resulting RNS Fourier transform provides an algorithm for performing circular convolutions characterized by flexibility in terms of length, computational cost ...
Pietro Burrascano +4 more
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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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Rheologica Acta, 1998
Oscillatory shear of polymeric liquids in the non-linear regime generates higher harmonic contributions in the shear stress response. These non-linear contributions are analyzed in Fourier space with respect to the different frequencies and intensities. Simulated and experimental Fourier rheology spectra for atactic poly(propylene) melts are shown.
Wilhelm, M., Maring, D., Spiess, H.
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Oscillatory shear of polymeric liquids in the non-linear regime generates higher harmonic contributions in the shear stress response. These non-linear contributions are analyzed in Fourier space with respect to the different frequencies and intensities. Simulated and experimental Fourier rheology spectra for atactic poly(propylene) melts are shown.
Wilhelm, M., Maring, D., Spiess, H.
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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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Randomization of the Fourier transform
Optics Letters, 2007We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.
Zhengjun, Liu, Shutian, Liu
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