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Backprojection with Fourier series expansion and FFT
International Conference on Acoustics, Speech, and Signal Processing, 2002A computerized tomography reconstruction technique with the fast Fourier transform (FFT) is discussed. A fast backprojection method through the use of interpolated FFT is presented. An approach to interpolating and backprojecting the convolved projections onto the image frame is proposed.
Makoto Tabei, Mitsuhiro Ueda
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Asymptotic Expansion of Multiple Fourier Transforms
SIAM Journal on Mathematical Analysis, 1979Asymptotic expansion of multi-dimensional Fourier transforms is derived. An explicit expression for the remainder term is also given, from which an error bound can readily be obtained.
Shivakumar, P. N., Wong, R.
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Fourier Series Expansion of Stochastic Measures
Theory of Probability & Its Applications, 2018zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Converse problems of Fourier expansion and their applications
Nonlinear Analysis: Theory, Methods & Applications, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Zhang, Chuanyi, Yao, Huili
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Backprojection with fourier series expansion and FFT
Systems and Computers in Japan, 1991AbstractThe filtered backprojection (FBP) method has recently been used for almost all the practical CT scanners because of its simple principle and high accuracy in reconstruction of images. However, it is difficult to use this method for some applications such as a real time display in which images are adjusted during displaying images, since a ...
Makoto Tabei +2 more
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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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Generalized Fourier Expansions.
1950PhD ; Mathematics ; University of Michigan, Horace H. Rackham School of Graduate Studies ; http://deepblue.lib.umich.edu/bitstream/2027.42/182869/2/0001524 ...
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Thermal Expansion on Stokes–Fourier Systems
SIAM Journal on Mathematical Analysis, 2012We prove the global solvability of an initial boundary value problem for the Stokes–Fourier system when the thermal expansion makes a nonincompressibility behavior. The natural convection including Oberbeck–Boussinesq effects appears as its primordial application.
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FOURIER EXPANSIONS WITH MODULAR FORM COEFFICIENTS
International Journal of Number Theory, 2009In this paper, we study the Fourier expansion where the coefficients are given as the evaluation of a sequence of modular forms at a fixed point in the upper half-plane. We show that for prime levels l for which the modular curve X0(l) is hyperelliptic (with hyperelliptic involution of the Atkin–Lehner type) then one can choose a sequence of weight k (
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