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Fourier series

About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.


Papers
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Journal ArticleDOI
TL;DR: In this paper, the current distribution on a thin circular loop transmitting antenna driven by a delta function generator is determined by Fourier series expansion, which is shown to be due to an inadequate approximation.
Abstract: The current distribution on a thin circular loop transmitting antenna driven by a delta‐function generator is determined approximately by Fourier series expansion. A difficulty encountered in previous analysis is shown to be due to an inadequate approximation.

162 citations

Journal ArticleDOI
TL;DR: In this article, the second and third virial coefficients of a classical monatomic adsorbate are put into a form suitable for numerical evaluation, which is accomplished by expanding the Boltzmann factors in the general expressions as Fourier series in the translational symmetry coordinates of the surface lattice.

160 citations

Journal ArticleDOI
TL;DR: Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.
Abstract: Fourier decomposition of a given amplitude distribution into plane waves and the subsequent superposition of these waves after propagation is a powerful yet simple approach to diffraction problems. Many vector diffraction problems can be formulated in this way, and the classical results are usually the consequence of a stationary-phase approximation to the resulting integrals. For situations in which the approximation does not apply, a factorization technique is developed that substantially reduces the required computational resources. Numerical computations are based on the fast-Fourier-transform algorithm, and the practicality of this method is shown with several examples.

160 citations

Book ChapterDOI
28 Jun 1999
TL;DR: It is shown that joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity gives better registration results than using either constraint alone or none at all.
Abstract: A fundamental problem with a large class of image registration techniques is that the estimated transformation from image A to B does not equal the inverse of the estimated transform from B to A. This inconsistency is a result of the matching criteria's inability to uniquely describe the correspondences between two images. This paper seeks to overcome this limitation by jointly estimating the transformation from A to B and from B to A while enforcing the consistency constraint that these transforms are inverses of one another. The transformations are further restricted to preserve topology by constraining them to obey the laws of continuum mechanics. A new parameterization of the transformation based on a Fourier series in the context of linear elasticity is presented. Results are presented using both Magnetic Resonance and X-ray Computed Tomography Imagery. It is shown that joint estimation of a consistent set of forward and reverse transformations constrained by linear-elasticity gives better registration results than using either constraint alone or none at all.

160 citations

Book
01 Jan 1986
TL;DR: In this article, the Lagrangian calculus and Fourier series have been studied in the Eighteenth Century, and the history of Dirichlet's Principle has been discussed in detail.
Abstract: 1: The Elements of Analysis in the Eighteenth Century.- 2: The Lagrangian Calculus and Fourier Series.- 3: New Trends in Rigor.- 4: Complex Functions and Integration.- 5: The Convergence of Fourier Series.- 6: Riemann's Theory of Functions.- 7: The Arithmetization of Analysis.- Appendix: On the History of "Dirichlet's Principle.

159 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023270
2022702
2021511
2020510
2019589
2018580