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Titlebook: Numerical Fourier Analysis; Gerlind Plonka,Daniel Potts,Manfred Tasche Book 20181st edition Springer Nature Switzerland AG 2018 fourier an

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发表于 2025-3-21 17:45:13 | 显示全部楼层 |阅读模式
书目名称Numerical Fourier Analysis
编辑Gerlind Plonka,Daniel Potts,Manfred Tasche
视频video
概述First unified presentation of Fourier theory and corresponding algorithms.Covers many recent highly recognized developments in numerical Fourier analysis.The code of most of the presented algorithms i
丛书名称Applied and Numerical Harmonic Analysis
图书封面Titlebook: Numerical Fourier Analysis;  Gerlind Plonka,Daniel Potts,Manfred Tasche Book 20181st edition Springer Nature Switzerland AG 2018 fourier an
描述.This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods...It starts with a detailed discussion of classical Fourier theory to enable readers to grasp the construction and analysis of advanced fast Fourier algorithms introduced in the second part, such as  nonequispaced  and sparse FFTs in higher dimensions...Lastly, it contains a selection of numerical applications, including recent research results on nonlinear function approximation by exponential sums...The code of most of the presented algorithms is available in the authors’ public domain software packages..Students and researchers alike benefit from this unified presentation of Fourier theory and corresponding algorithms..
出版日期Book 20181st edition
关键词fourier analysis; fourier series; fourier transforms; discrete fourier transforms; fast fourier transfor
版次1
doihttps://doi.org/10.1007/978-3-030-04306-3
isbn_ebook978-3-030-04306-3Series ISSN 2296-5009 Series E-ISSN 2296-5017
issn_series 2296-5009
copyrightSpringer Nature Switzerland AG 2018
The information of publication is updating

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发表于 2025-3-21 20:47:53 | 显示全部楼层
Fourier Transforms, Hermite functions, which form an orthogonal basis of ., are eigenfunctions of the Fourier transform. In Sect. 2.3, we present the Poisson summation formula and Shannon’s sampling theorem. Finally, two generalizations of the Fourier transform are sketched in Sect. 2.5, namely the windowed Fourier transform and the fractional Fourier transform.
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发表于 2025-3-22 04:57:27 | 显示全部楼层
2296-5009 rier analysis.The code of most of the presented algorithms i.This book offers a unified presentation of Fourier theory and corresponding algorithms emerging from new developments in function approximation using Fourier methods...It starts with a detailed discussion of classical Fourier theory to ena
发表于 2025-3-22 11:17:26 | 显示全部楼层
Fourier Series,describe the Gibbs phenomenon for partial sums of the Fourier series of . near a jump discontinuity. Finally, in Sect. 1.5, we apply Fourier series in digital signal processing and describe the linear filtering of discrete signals.
发表于 2025-3-22 13:52:19 | 显示全部楼层
Chebyshev Methods and Fast DCT Algorithms,ls, which are given in the orthogonal basis of Chebyshev polynomials. We present fast DCT algorithms in Sect. 6.3. These fast DCT algorithms are based either on the FFT or on the orthogonal factorization of the related cosine matrix.
发表于 2025-3-22 21:02:59 | 显示全部楼层
发表于 2025-3-22 22:55:58 | 显示全部楼层
Gerlind Plonka,Daniel Potts,Gabriele Steidl,Manfred Tascheanalyze the above problems with respect to crisp (exact) parameters...However, in real-lifeapplications such as for biological problems, it is not always possible to get exact values of the associated parameters due to errors in measurements/experiments, observations, and many other errors. Therefor
发表于 2025-3-23 04:08:18 | 显示全部楼层
Discrete Fourier Transforms,ier matrix. We show that block circulant matrices can be diagonalized by Kronecker products of Fourier matrices. Finally, Sect. 3.5 addresses real versions of the DFT, such as the discrete cosine transform (DCT) and the discrete sine transform (DST). These linear transforms are generated by orthogon
发表于 2025-3-23 08:18:28 | 显示全部楼层
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