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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.


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01 Jan 1975
TL;DR: This paper presents a meta-modelling procedure called “Smart Card” which automates the very laborious and therefore time-heavy and expensive and expensive process of manually cataloging and cataloging the components of a computer.
Abstract: Review of least squares, orthogonality and the Fourier series review of continuous transforms transfer functions and convolution sampling and measurement of signals the discrete Fourier transform the fast Fourier transform the z-transform non-recursive digital systems digital and continuous systems simulation of continuous systems analogue and digital filter design review of random functions correlation and power spectra least-squares system design random sequences and spectral estimation.

286 citations

Journal ArticleDOI
TL;DR: In this article, the effective medium theory of one-dimensional and two-dimensional periodic structures is investigated, and a method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first-, and secondorder effective indices.
Abstract: The effective medium theory of one-dimensional and two-dimensional periodic structures are investigated. A method based on a Fourier decomposition of the wave propagating along the direction perpendicular to the periodic structures allows one to determine the zeroth-, first- and second-order effective indices. For one-dimensional problems, we derive closed-form expressions of the effective indices for both TE and TM polarization. Our result can be applied to arbitrary periodic structure with symmetric or non-symmetric lamellar or continuously varying index profiles. The theoretical predictions are carefully validated using rigorous coupled-wave analysis. For the two-dimensional case, only symmetric structures are discussed and the computation of the zeroth-, first-, and second-order effective indices requires the inversion of an infinite matrix which can be truncated and simply solved numerically. The EMT prediction is qualitatively validated using rigorous computation for small period-to-wavelen...

283 citations

Journal ArticleDOI
TL;DR: In this article, Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1 and an optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints.

279 citations


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