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Fourier Series Formalization in ACL2(r) [PDF]
Electronic Proceedings in Theoretical Computer Science, 2015 We formalize some basic properties of Fourier series in the logic of ACL2(r), which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis.
Cuong K. Chau +2 more
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Statistical inference on nonparametric regression model with approximation of Fourier series function: Estimation and hypothesis testing [PDF]
MethodsXNonparametric regression is an approximation method in regression analysis that is not constrained by the assumption of knowing the regression curve. One of the functions to approximate the curve is a Fourier series function. The nonparametric regression
Mustain Ramli +2 more
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The minimality of mean square error in chirp approximation using fractional fourier series and fractional fourier transform [PDF]
Scientific Reports, 2022 Chirps are familiar in nature, have a built-in resistance to noise and interference, and are connected to a wide range of highly oscillatory processes.
Omar T. Bafakeeh +9 more
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On Fourier Series of Fuzzy-Valued Functions [PDF]
The Scientific World Journal, 2014 Fourier analysis is a powerful tool for many problems, and especially for solving various differential equations of interest in science and engineering.
Uğur Kadak, Feyzi Başar
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CQD Revista Eletrônica Paulista de Matemática, 2016 O objetivo principal deste trabalho é apresentar alguns pontos importantes da teoria da Análise de Fourier. Na primeira seção descrevemos a trajetória de Fourier, um dos matemáticos mais citados do século XX. A seção seguinte introduz a Série de Fourier
Felipe Felix Souto, Marta Cilene Gadotti
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A Didactic and Visual Approach to the Fourier Transform
Revista Brasileira de Ensino de Física, 2023 This work provides a comprehensive derivation of the Fourier transform, with less emphasis on the mathematical rigor associated with the theory. Instead, its primary goal is to serve as a didactic resource that fosters an understanding of various ...
Daniel José Kmita +1 more
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Notes regarding classical Fourier series
Journal of Numerical Analysis and Approximation Theory, 2023 A survey of some classical results from the theory of trigonomtrical series is presented, especially the case of Fourier series. Some new proofs are presented, and Riemann's theory of trigonometrical series is is given special attention.
Paul Bracken
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Alternative Method to Estimate the Fourier Expansions and Its Rate of Change
Mathematics, 2022 This paper presents a methodology to obtain the Fourier coefficients (FCs) and the derivative Fourier coefficients (DFCs) from an input signal. Based on the Taylor series that approximates the input signal into a trigonometric signal model through the ...
Johnny Rodríguez-Maldonado +2 more
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Matrix Summability of Walsh–Fourier Series
Mathematics, 2022 The presented paper discusses the matrix summability of the Walsh–Fourier series. In particular, we discuss the convergence of matrix transforms in L1 space and in CW space in terms of modulus of continuity and matrix transform variation.
Ushangi Goginava, Károly Nagy
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Quantization of pseudo-differential operators on the torus [PDF]
, 2008 Pseudo-differential and Fourier series operators on the n-torus are analyzed by using global representations by Fourier series instead of local representations in coordinate charts.
Ruzhansky, Michael, Turunen, Ville
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