Applications of the Fourier transforms

Wang, Ruye

doi:10.1017/cbo9781139015158.007

Cited by 6 publications

(10 citation statements)

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“…where the rectangular function Rect(ϕ/Φ) = θ(ϕ + Φ/2) − θ(ϕ − Φ/2) and θ(·) the Heaviside function [32],…”

Section: Modified Electromagnetic Wave Propagationmentioning

confidence: 99%

Vacuum high-harmonic generation in the shock regime

Böhl¹,

King²,

Rühl³

2015

Phys. Rev. A

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Electrodynamics becomes nonlinear and permits the self-interaction of fields when the quantised nature of vacuum states is taken into account. The effect on a plane probe pulse propagating through a stronger constant crossed background is calculated using numerical simulation and by analytically solving the corresponding wave equation. The electromagnetic shock resulting from vacuum high harmonic generation is investigated and a nonlinear shock parameter identified.

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“…where the rectangular function Rect(ϕ/Φ) = θ(ϕ + Φ/2) − θ(ϕ − Φ/2) and θ(·) the Heaviside function [32],…”

Section: Modified Electromagnetic Wave Propagationmentioning

confidence: 99%

Vacuum high-harmonic generation in the shock regime

Böhl¹,

King²,

Rühl³

2015

Phys. Rev. A

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“…For the scenarios tested, this occurs at approximately every 140 kHz, separating frequencies in batches. This is a result of the input spectrum from the thermal pulse the system is subject to [16]. The Fourier transform of a rectangular pulse having a pulse duration τ ¼ 7.2 μs and an arbitrary amplitude A ¼ 1 can be expressed by GðfÞ ¼ sinðπfτÞ πf : ð13Þ Figure 13 shows the Fourier transform result for longitudinal strain for all rod radii simulated, plotted along with the absolute values of the scaled input spectrum for a rectangular pulse according to Eq.…”

Section: Numerical Modeling-comparison Between Thermostructural mentioning

confidence: 99%

Numerical simulation of long rods impacted by particle beams

Portelli

Bertarelli

Carra

et al. 2018

Phys. Rev. Accel. Beams

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Analytical solutions detailing the propagation of longitudinal waves in slender rods subjected to a sudden increase of internal energy provide simple tools for the calculation of the temperature distribution in impacted rods as well as the resulting mechanical response. The topic is of great interest in particle accelerator technology, especially with regards to collimation systems, where beam intercepting devices can be generally approximated to one-dimensional (1D) elements potentially subjected, in accidental scenarios, to abrupt thermal energy depositions induced by the impacting particles. In this study, two finite element numerical models are presented and compared to the analytical solutions by Bertarelli, Dallocchio and Kurtyka, discussing the rapid temperature increase in slender rods due to particle beam impacts and the resulting dynamic longitudinal response. The first model is a sequentially coupled thermomechanical analysis; the second is based on a modal analysis to find the harmonic response of the system. The results indicate that phenomena neglected in analytical solutions, primarily dispersion of the longitudinal wave due to interactions with the free external surface of the rod, can be included in numerical models and can be observed in simulation results. The study further shows how numerical methods can be utilized to predict the frequencies and amplitudes of high-frequency disturbances in the longitudinal wave signal, and how these effects can be mitigated in preparation for experimental scenarios by fine-tuning the geometry of the rod and varying the duration of the pulse. This is especially useful with regards to experiments conducted in the HiRadMat facility at CERN, such as the recently conducted HRMT36 experiment, where highfrequency components can distort the signal to be observed.

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“…The last decade based on orthogonal transform has been seen a quiet revolution in digital video technology such as Moving Picture Experts Group (MPEG)-4, H.264, and high efficiency video coding (HEVC) [1][2][3][4][5][6][7]. Digital video is everywhere such as DVD, gaming players, computers and mobile handsets.…”

Section: Introductionmentioning

confidence: 99%

“…Video compression is essential to all these applications. The discrete cosine transform (DCT)-II is popular compression structures for MPEG-4, H.264, and HEVC, and is accepted as the best suboptimal transformation since its performance is very close to that of the statistically optimal Karhunen-Loeve transform (KLT) [1][2][3][4][5]. For practical consideration, the underlying H.264-advanced video coding (AVC) intra mode dictates the transform coding implementation within a block coder with a typical block of size up to 16 Â 16.…”

Section: Introductionmentioning

confidence: 99%

“…It has been shown that this matrix decomposition is useful in developing the fast algorithms and characters [20]. Individual DCT-II [1][2][3]6,7,12], DST-II [4,6,7,13], DFT [3,5,14], and HWT [9] matrices can be decomposed to one orthogonal character matrix and a corresponding special sparse matrix. The inverse of the sparse matrix can be easily obtained from the property of the block (element)-wise inverse Jacket matrix.…”

Section: Introductionmentioning

confidence: 99%

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A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

Lee

Khan

Kim

et al. 2014

Signal Processing: Image Communication

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In this paper, based on the block (element)-wise inverse Jacket matrix, a unified fast hybrid diagonal block-wise transform (FHDBT) algorithm is proposed. A new fast diagonal block matrix decomposition is made by the matrix product of successively lower order diagonal Jacket matrix and Hadamard matrix. Using a common lower order matrix in the form of 1 1, a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/DST-II compression scheme compared with the DCT-II only compression method. Signal Processing: Image CommunicationThis work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. , a fast recursive structure can be developed in the FHDBT, which is able to convert a newly developed discrete cosine transform (DCT)-II, discrete sine transform (DST)-II, discrete Fourier transform (DFT), and Haar-based wavelet transform (HWT). Since these DCT-II, DST-II, DFT, and HWT are widely used in different areas of applications, the proposed FHDBT can be applied to the heterogeneous system requiring several transforms simultaneously. Comparing with pre-existing DCT-II, DST-II, DFT, and HWT, it is shown that the proposed FHDBT exhibits less the complexity as its matrix size gets larger. The proposed algorithm is also well matched to circulant channel matrix. From the numerical experiments, it is shown that a better performance can be achieved by the use of DCT/ DST-II compression scheme compared with the DCT-II only compression method.

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Applications of the Fourier transforms

Cited by 6 publications

References 0 publications

Vacuum high-harmonic generation in the shock regime

Vacuum high-harmonic generation in the shock regime

Numerical simulation of long rods impacted by particle beams

A fast hybrid Jacket–Hadamard matrix based diagonal block-wise transform

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