Results 261 to 270 of about 24,683 (302)
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2014
In Chap. 1, it was shown, mostly by using graphics, that various waves can be expressed by a summation of sine and cosine functions, i.e., by the Fourier series (see Eq. 1.5). In this chapter, first, a method of determining coefficients of Fourier series will be given. A key idea is the integral of the products of sine and cosine functions.
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In Chap. 1, it was shown, mostly by using graphics, that various waves can be expressed by a summation of sine and cosine functions, i.e., by the Fourier series (see Eq. 1.5). In this chapter, first, a method of determining coefficients of Fourier series will be given. A key idea is the integral of the products of sine and cosine functions.
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A Series Expansion of the Fourier Integral
Proceedings of the IRE, 1951Evaluation of the Fourier integral by parts leads to two different series representations of a time function in the frequency domain. These series involve powers of the frequency variable and either derivatives or integrals of the function, evaluated at the upper time limit only. It is necessary that the function so treated be analytic between the time
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Backprojection by upsampled Fourier series expansion and interpolated FFT
IEEE Transactions on Image Processing, 1992A fast backprojection method through the use of interpolated fast Fourier transform (FFT) is presented. The computerized tomography (CT) reconstruction by the convolution backprojection (CBP) method has produced precise images. However, the backprojection part of the conventional CBP method is not very efficient.
Makoto Tabei, Mitsuhiro Ueda
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Improved Fourier series expansion methods for electrocardiography analysis
2015 IEEE International Conference on Digital Signal Processing (DSP), 2015In this work, we propose two Fourier series expansion methods (FSEM), one improved from the original FSEM and another a simplified version of the improved FSEM, to significantly enhance the accuracy of solution along with consuming less computation time and to eliminate the Gibbs phenomenon when dealing with electrocardiography (ECG).
Ming-Lun Lee +4 more
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Evaluation of Multinormal Probabilities Using Fourier Series Expansions
Applied Statistics, 1985With the aid of Fourier series expansions, the probability integral is converted to one having infinite limits. An algorithm is then developed to evaluate the resulting integral.
Russell, N. S. +2 more
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Fourier series expansion method for plated-structures
Structural Engineering and Mechanics, 1999This work applies a structural analysis method based on an analytical solution from the Fourier series which transforms a half-range cosine expansion into a static solution involving plated structures. Two sub-matrices of in-plane and plate-bending problems are also formulated and coupled with the prescribed boundary conditions for these variables ...
Jiann-Gang Deng, Fu-Ping Cheng
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Uniform convergence of expansions into a multiple trigonometric Fourier series or a Fourier integral
Mathematical Notes of the Academy of Sciences of the USSR, 1975Questions of convergence almost everywhere of expansions into a multiple trigonometric Fourier series or a Fourier integral are studied for functions from Lp, p≥1, with summation over rectangles. Moreover, a “generalized localization principle,” understood in the sense of convergence almost everywhere, is considered in the paper.
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Fourier series expansion and DFT on a moving window
[Proceedings] IECON '90: 16th Annual Conference of IEEE Industrial Electronics Society, 2002The recursive calculation of Fourier series spectra and the discrete Fourier transform (DFT) on a moving window is investigated. The basic problem is to calculate the spectra coefficients on a one-step-shifted-to-the-right window using the old coefficient values. Several formulas are presented giving the adaptation law of the time-varying spectra.
L. Homssi, A. Despujols
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Expansion of Continuous Differentiable Functions in Fourier Legendre Series
Canadian Journal of Mathematics, 1967Let1.1denote the nth partial sum of the Fourier Legendre series of a function ƒ(x). The references available to us, except (5), prove only that Sn(ƒ, x) converges uniformly to ƒ(x) in [— 1, 1] if ƒ(x) has a continuous second derivative on [—1, 1]. Very recently Suetin (5) has shown by employing a theorem of A. F.
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Mathematics of the USSR-Izvestiya, 1976
In this work there are constructed a function such that the difference between the Fourier series expansion and the Fourier integral expansion for summation over squares diverges almost everywhere on , and a function , , , for which the difference diverges at a point.Bibliography: 5 titles.
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In this work there are constructed a function such that the difference between the Fourier series expansion and the Fourier integral expansion for summation over squares diverges almost everywhere on , and a function , , , for which the difference diverges at a point.Bibliography: 5 titles.
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