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Modeling a Periodic Signal Using Fourier Series
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作者 Uwaydah Leith 《Journal of Applied Mathematics and Physics》 2024年第3期841-860,共20页
This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a ... This paper covers the concept of Fourier series and its application for a periodic signal. A periodic signal is a signal that repeats its pattern over time at regular intervals. The idea inspiring is to approximate a regular periodic signal, under Dirichlet conditions, via a linear superposition of trigonometric functions, thus Fourier polynomials are constructed. The Dirichlet conditions, are a set of mathematical conditions, providing a foundational framework for the validity of the Fourier series representation. By understanding and applying these conditions, we can accurately represent and process periodic signals, leading to advancements in various areas of signal processing. The resulting Fourier approximation allows complex periodic signals to be expressed as a sum of simpler sinusoidal functions, making it easier to analyze and manipulate such signals. 展开更多
关键词 fourier series Signal PERIODIC PERIOD Frequency SINE COSINE CONVERGENCE
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Improved Responses with Multitaper Spectral Analysis for Magnetotelluric Time Series Data Processing:Examples from Field Data
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作者 Matthew J.COMEAU Rafael RIGAUD +2 位作者 Johanna PLETT Michael BECKEN Alexey KUVSHINOV 《Acta Geologica Sinica(English Edition)》 SCIE CAS CSCD 2024年第S01期14-17,共4页
In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without ... In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra. 展开更多
关键词 MAGNETOTELLURICS electrical resistivity time series PROCESSING fourier analysis multitaper
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ASYMPTOTIC BEHAVIOR OF ECKHOFF'S METHOD FOR FOURIER SERIES CONVERGENCE ACCELERATION 被引量:2
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作者 A.Barkhudaryan R.Barkhudaryan A.Poghosyan 《Analysis in Theory and Applications》 2007年第3期228-242,共15页
The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczo... The current paper considers the problem of recovering a function using a limited number of its Fourier coefficients. Specifically, a method based on Bernoulli-like polynomials suggested and developed by Krylov, Lanczos, Gottlieb and Eckhoff is examined. Asymptotic behavior of approximate calculation of the so-called "jumps" is studied and asymptotic L2 constants of the rate of convergence of the method are computed. 展开更多
关键词 fourier series convergence acceleration Bemoulli polynomials
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Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain 被引量:1
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作者 WANG SHU-YUNI LIANG XUEoZHANG +1 位作者 FU YAO SUN XUE-NAN 《Communications in Mathematical Research》 CSCD 2009年第2期104-114,共11页
A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn(f; t) of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove t... A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn(f; t) of generalized Fourier series on a parallel hexagon domain Ω associating with threedirection partition. We prove that an operator Wn(f; t) with the new kernel function converges uniformly to any continuous function f(t) ∈ Cn(Ω) (the space of all continuous functions with period Ω) on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function. 展开更多
关键词 three-direction coordinate kernel function generalized fourier series uniform convergence
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Alternative Fourier Series Expansions with Accelerated Convergence 被引量:1
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作者 Wenlong Li 《Applied Mathematics》 2016年第15期1824-1845,共23页
The key objective of this paper is to improve the approximation of a sufficiently smooth nonperiodic function defined on a compact interval by proposing alternative forms of Fourier series expansions. Unlike in classi... The key objective of this paper is to improve the approximation of a sufficiently smooth nonperiodic function defined on a compact interval by proposing alternative forms of Fourier series expansions. Unlike in classical Fourier series, the expansion coefficients herein are explicitly dependent not only on the function itself, but also on its derivatives at the ends of the interval. Each of these series expansions can be made to converge faster at a desired polynomial rate. These results have useful implications to Fourier or harmonic analysis, solutions to differential equations and boundary value problems, data compression, and so on. 展开更多
关键词 fourier series Trigonometric series fourier Approximation Convergence Acceleration
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CONVERGENCE OF LOGARITHMIC MEANS OF MULTIPLE WALSH-FOURIER SERIES 被引量:1
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作者 G.Gát U.Goginava G.Tkebuchava 《Analysis in Theory and Applications》 2005年第4期326-338,共13页
Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L ([0, 1)d), d≥1 into space weak - LI([0,1)^d) are studied. The maximal Orlicz space such that the Norlund logarithmic means... Norlund logarithmic means of multiple Walsh-Fourier series acting from space L In^d-1 L ([0, 1)d), d≥1 into space weak - LI([0,1)^d) are studied. The maximal Orlicz space such that the Norlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found. 展开更多
关键词 Multiple Walsh-fourier series convergence in metric and in measure Norlund means
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APPROXIMATION OF CONVEX TYPE FUNCTION BY PARTIAL SUMS OF FOURIER SERIES
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作者 YuGuohua 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期67-76,共10页
The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function b... The concept of convex type function is introduced in this paper,from which a kin d of convex decomposition approach is proposed.As one of applications of this a pproach,the approximation of the convex type function by the partial sum of its Fourier series is inves tigated.Moreover,the order of approximation is describe d with the 2th continuous modulus. 展开更多
关键词 fourier series convex type function CONVEX DECOMPOSITION Riemann deriv ative continuous modulus approximation.
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Super-Fast Approximation Algorithms Using Classical Fourier Tools
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作者 Anry Nersessian 《Advances in Pure Mathematics》 2024年第7期596-618,共23页
In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered that knowledge of a finite... In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered that knowledge of a finite number of Fourier coefficients of function f from an infinite-dimensional set of elementary functions allows f to be accurately restored (the phenomenon of over-convergence). Below, parametric biorthogonal systems are constructed for classical trigonometric Fourier series, and the corresponding phenomena of over-convergence are discovered. The decisive role here was played by representing the space L2 as an orthogonal sum of two corresponding subspaces. As a result, fast parallel algorithms for reconstructing a function from its truncated trigonometric Fourier series are proposed. The presented numerical experiments confirm the high efficiency of these convergence accelerations for smooth functions. In conclusion, the main results of the work are summarized, and some prospects for the development and generalization of the proposed approaches are discussed. 展开更多
关键词 fourier series Acceleration of Convergence Parametric Biorthogonalization Spectral Methods Over-Convergence Phenomenon
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On the Efficacy of Fourier Series Approximations for Pricing European Options
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作者 A. S. Hurn K. A. Lindsay A. J. McClelland 《Applied Mathematics》 2014年第17期2786-2807,共22页
This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in... This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible. 展开更多
关键词 fourier Transform fourier series Characteristic Function OPTION PRICE
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Further Discussion on the Calculation of Fourier Series
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作者 Caixia Zhang 《Applied Mathematics》 2015年第3期594-598,共5页
Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine ... Fourier series is an important mathematical concept. It is well known that we need too much computation to expand the function into Fourier series. The existing literature only pointed that its Fourier series is sine series when the function is an odd function and its Fourier series is cosine series when the function is an even function. And on this basis, in this paper, according to the function which satisfies different conditions, we give the different forms of Fourier series and the specific calculation formula of Fourier coefficients, so as to avoid unnecessary calculation. In addition, if a function is defined on [0,a], we can make it have some kind of nature by using the extension method as needed. So we can get the corresponding form of Fourier series. 展开更多
关键词 fourier COEFFICIENTS Fouries series PERIOD series EXPANSION Extension
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Approximation by Nrlund Means of Hexagonal Fourier Series
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作者 Ali Guven 《Analysis in Theory and Applications》 CSCD 2017年第4期384-400,共17页
Let f be an H-periodic HOlder continuous function of two real variables.The error ||f-Nn (p;f)|| is estimated in the uniform norm and in the Holder norm,where p=(pk)k=0∞is a nonincreasing sequence of positive... Let f be an H-periodic HOlder continuous function of two real variables.The error ||f-Nn (p;f)|| is estimated in the uniform norm and in the Holder norm,where p=(pk)k=0∞is a nonincreasing sequence of positive numbers and Nn (p;f) is thenth Norlund mean of hexagonal Fourier series of f with respect to p = (pk)k∞=0. 展开更多
关键词 Hexagonal fourier series Holder class Norlund mean.
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Estimation of Winds at Different Isobaric Levels Based on the Observed Winds at 850 hPa Level Using Double Fourier Series
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作者 S. N. Bavadekar (1) R. M. Khaladkar (1) 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 1994年第3期327-334,共8页
A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds a... A technique based on the double Fourier series is developed to estimate the winds at different isobaric levels forthe limited area domain, 35°E to 140°E and 30°S to 40°N, using the observed winds at 850 hPa lcvcl for the month ofJune. For this purpose the wind field at a level under consideration is taken in the ratio form with that of 850 hPa level and the coefficients of the double Fouricr series are computed. These coefficients are subsequently used to computethe winds which are compared with the actual winds. The results of the double Fourier series technique are comparedwith those of the polynomial surface fitting method developed by Bavadekar and Khaladkar (1 992). The technique isalso applied for the daily wind data of 11. June, 1979 and the validation of the technique is tested for a few radiosondestations of india. The computed winds for these radiosonde stations arc quite close to observed winds. 展开更多
关键词 Double fourier series Objective analysis Cloud motion vectors Numerical weather prediction Polynomial surface fitting
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Fourier-Series Representation of Discontinuous Functions and Its Physical Applications
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作者 Sami M. Al-Jaber Iyad Saadeddin 《Applied Mathematics》 2019年第4期226-233,共8页
In this work, Fourier-series representation of a discontinuous function is used to highlight and clarify the controversial problem of finding the value of the function at a point of discontinuity. Several physical sit... In this work, Fourier-series representation of a discontinuous function is used to highlight and clarify the controversial problem of finding the value of the function at a point of discontinuity. Several physical situations are presented to examine the consequences of this kind of representation and its impact on some widely well-known problems whose results are not clearly understood or justified. 展开更多
关键词 Electric Field CHARGED CONDUCTORS ELECTROSTATICS fourier series
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On the Equiconvergence of the Fourier Series and Integral of Distributions
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作者 A. A. Rakhimov 《Journal of Applied Mathematics and Physics》 2015年第11期1361-1366,共6页
We prove equiconvergence of the Bochner-Riesz means of the Fourier series and integral of distributions with compact support from the Liouville spaces.
关键词 Bochner-Riesz Means fourier series fourier INTEGRALS DISTRIBUTIONS Equiconvergence
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UNIFORM CONVERGENCE OF CES■RO MEANS OF NEGATIVE ORDER OF DOUBLE TRIGONOMETRIC FOURIER SERIES
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作者 U.Goginava 《Analysis in Theory and Applications》 2007年第3期255-265,共11页
In this paper we prove that if f ∈ C ([-π, π]^2) and the function f is bounded partial p-variation for some p ∈[1, +∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) ... In this paper we prove that if f ∈ C ([-π, π]^2) and the function f is bounded partial p-variation for some p ∈[1, +∞), then the double trigonometric Fourier series of a function f is uniformly (C;-α,-β) summable (α+β 〈 1/p,α,β 〉 0) in the sense of Pringsheim. If α + β ≥ 1/p, then there exists a continuous function f0 of bounded partial p-variation on [-π,π]^2 such that the Cesàro (C;-α,-β) means σn,m^-α,-β(f0;0,0) of the double trigonometric Fourier series of f0 diverge over cubes. 展开更多
关键词 fourier series bounded variation. Cesàro means
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LEGENDRE SERIES SOLUTIONS FOR TIME-VARIATION DYNAMICS
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作者 Cao, ZY Zou, GP Tang, SG 《Acta Mechanica Solida Sinica》 SCIE EI 2000年第1期60-66,共7页
In this topic, a new. approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-var... In this topic, a new. approach to the analysis of time-variation dynamics is proposed by use of Legendre series expansion and Legendre integral operator matrix. The theoretical basis for effective solution of time-variation dynamics is therefore established, which is beneficial to further research of time-variation science. 展开更多
关键词 time-variation dynamics Legendre series state space equation integral operator matrix
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Estimation of permafrost thermal behavior using Fourier series model
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作者 ZHANG Yan-yu ZANG Shu-ying +3 位作者 ZHAO Lin MA Da-long LIN Yue LI Hao 《Journal of Mountain Science》 SCIE CSCD 2022年第3期715-725,共11页
Permafrost,being an important component of the cryosphere,is sensitive to climate change.Therefore,it is necessary to investigate the change of temperature within permafrost.In this study,we proposed a Fourier series ... Permafrost,being an important component of the cryosphere,is sensitive to climate change.Therefore,it is necessary to investigate the change of temperature within permafrost.In this study,we proposed a Fourier series model derived from the conduction equation to simulate permafrost thermal behavior over a year.The boundary condition was represented by the Fourier series and the geothermal gradient.The initial condition was represented as a linear function relative to the geothermal gradient.A comparative study of the different models(sinusoidal model,Fourier series model,and the proposed model)was conducted.Data collected from the northern Da Xing’anling Mountains,Northeast China,were applied for parameterization and validation for these models.These models were compared with daily mean ground temperature from the shallow permafrost layer and annual mean ground temperature from the bottom permafrost layer,respectively.Model performance was assessed using three coefficients of accuracy,i.e.,the mean bias error,the root mean square error,and the coefficient of determination.The comparison results showed that the proposed model was accurate enough to simulate temperature variation in both the shallow and bottom permafrost layer as compared with the other two Fourier series models(sinusoidal model and Fourier model).The proposed model expanded on a previous Fourier series model for which the initial and bottom boundary conditions were restricted to being constant. 展开更多
关键词 PERMAFROST Da Xing’anling Mountains Ground temperature fourier series model
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An Approximation for the Doppler Broadening Function and Interference Term Using Fourier Series
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作者 Alessandro da C. Goncalves Daniel A. P. Palma Aquilino S. Martinez 《World Journal of Nuclear Science and Technology》 2012年第4期144-149,共6页
The calculation of the Doppler broadening function and of the interference term are important in the generation of nuclear data. In a recent paper, Goncalves and Martinez proposed an analytical approximation for the c... The calculation of the Doppler broadening function and of the interference term are important in the generation of nuclear data. In a recent paper, Goncalves and Martinez proposed an analytical approximation for the calculation of both functions based in sine and cosine Fourier transforms. This paper presents new approximations for these functions, and , using expansions in Fourier series, generating expressions that are simple, fast and precise. Numerical tests applied to the calculation of scattering average cross section provided satisfactory accu- racy. 展开更多
关键词 Doppler BROADENING FUNCTION fourier series New Formulation for the INTERFERENCE
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APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE FOURIER INTEGRALS AND FOURIER SERIES ON SET OF FULL MEASURE
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作者 Wang Shiming Zhejiang Institute of Technology, China Math. Section Dept. of Basic Courses Zhejiang Institute of Technology, Hangzhou, 310014, China 《Analysis in Theory and Applications》 1994年第2期17-23,共7页
In this paper we consider the approximation for functions in some subspaces of L^2 by spherical means of their Fourier integrals and Fourier series on set of full measure. Two main theorems are obtained.
关键词 SET Th Pro APPROXIMATION OF SPHERICAL MEANS OF MULTIPLE fourier INTEGRALS AND fourier series ON SET OF FULL MEASURE WANG
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SUMMATION OF TRIGONOMETRIC SERIES BY FOURIER TRANSFORMS
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作者 钱伟长 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1989年第5期385-397,共13页
This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms. By means of the known results of Fourier transforms, many difficult and complex problems of summation... This paper gives the theorems concerning the summation of trigonometric series with the help of Fourier transforms. By means of the known results of Fourier transforms, many difficult and complex problems of summation of trigonometric series can be solved. This method is a comparatively unusual way to find the summation of trigonometric series, and has been used to establish the comprehensive table of summation of trigonometric series. In this table 10 thousand scries arc given, and most of them are new. 展开更多
关键词 exp SUMMATION OF TRIGONOMETRIC series BY fourier TRANSFORMS
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