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1.
Computation of the fractional Fourier transform 总被引:1,自引:0,他引:1
Adhemar Bultheel Hctor E. Martínez Sulbaran 《Applied and Computational Harmonic Analysis》2004,16(3):182-202
In this paper we make a critical comparison of some
programs for the digital computation of the fractional Fourier transform that are freely available and we describe our own implementation that filters the best out of the existing ones. Two types of transforms are considered: first, the fast approximate fractional Fourier transform algorithm for which two algorithms are available. The method is described in [H.M. Ozaktas, M.A. Kutay, G. Bozda
i, IEEE Trans. Signal Process. 44 (1996) 2141–2150]. There are two implementations: one is written by A.M. Kutay, the other is part of package written by J. O'Neill. Second, the discrete fractional Fourier transform algorithm described in the master thesis by Ç. Candan [Bilkent University, 1998] and an algorithm described by S.C. Pei, M.H. Yeh, and C.C. Tseng [IEEE Trans. Signal Process. 47 (1999) 1335–1348]. 相似文献
2.
Avram Sidi 《Applied mathematics and computation》2010,216(11):3378-3385
In this work, we are concerned with the derivation of full asymptotic expansions for Fourier integrals as s → ∞, where s is real positive, [a, b] is a finite interval, and the functions f(x) may have different types of algebraic and logarithmic singularities at x = a and x = b. This problem has been treated in the literature by techniques involving neutralizers and Mellin transforms. Here, we derive the relevant asymptotic expansions by a method that employs simpler and less sophisticated tools. 相似文献
3.
本文研究连续窗口Fourier变换的反演公式.与经典的积分重构公式不同,本文证明当窗函数满足合适的条件时,窗口Fourier变换的反演公式可以表示为一个离散级数.此外,本文还研究这一重构级数的逐点收敛及其在Lebesgue空间的收敛性.对于L^2空间,本文给出重构级数收敛的充分必要条件. 相似文献
4.
Michael E. Taylor 《Proceedings of the American Mathematical Society》2001,129(7):2001-2003
In this note we complete a circle of results presented in §5 of an earlier work of the author (J. Fourier Anal. 5 (1999), 449-463), establishing the endpoint case of Proposition 10 of that paper. As a consequence, we have results on pointwise convergence of the Fourier series (summed by spheres) of a function on the 3-dimensional torus with a simple jump across a smooth surface , with no curvature hypotheses on , extending Proposition 7 of that paper.
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Hou-Yi Chen 《代数通讯》2013,41(1):263-266
Let X be a smooth complex projective 3-fold of general type. We give effective upper bounds for the order of the automorphism group of X under certain conditions. 相似文献
7.
Daniel M. Oberlin 《Proceedings of the American Mathematical Society》2004,132(4):1195-1199
We establish a uniform Fourier restriction estimate for certain hypersurfaces in .
8.
Let * denote convolution and let x denote the Dirac measureat a point x. A function in L2(R)) is called a difference oforder 1 if it is of the form g-x * g for some x R and g L2(R)).Also, a difference of order 2 is a function of the form for some x R and g L2(R)). In fact,the concept of a difference of order s may bedefined in a similar manner for each s 0. If f denotes the Fouriertransform of f, it is known that a function f in L2(R)) is afinite sum of differences of order s if and only if , and the vector space of all suchfunctions is denoted by Ds (L2(R)). Every function in Ds (L2(R))is a sum of int(2s) + 1 differences of order s, where int(t)denotes the integer part of t. Thus, every function in D1 (L2(R))is a sum of three first order differences, but it was provedin 1994 that there is a function in D1 (L(R)) which is neverthe sum of two first order differences. This complemented, forthe group R, the corresponding result for first order differencesobtained by Meisters and Schmidt in 1972 for the circle group.The results show that there is a function in L2 R such that,for each s 1/2, this function is a sum of int (2s) + 1 differencesof order s but it is never the sum of int (2s) differences oforder s. The proof depends upon extending to higher dimensionsthe following result in two dimensions obtained by Schmidt in1972 in connection with Heilbronn's problem: if x1, x_n arepoints in the unit square, Following on from the work of Meisters and Schmidt, this workfurther develops a connection between certain estimates in combinatorialgeometry and some questions of sharpness in harmonic analysis.2000 Mathematics Subject Classification 42A38 (primary), 52A40(secondary). 相似文献
9.
Let be a discrete subgroup of SL(2,
) with a fundamental region of finite hyperbolic volume. (Then, is a finitely generated Fuchsian group of the first kind.) Let
0}} {a(n)e^{2\pi i(n + {\kappa })z/{\lambda }} } ,{ }z \in \mathcal{H}.$$
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be a nontrivial cusp form, with multiplier system, with respect to . Responding to a question of Geoffrey Mason, the authors present simple proofs of the following two results, under natural restrictions upon .
Theorem.
If the coefficients a(n) are real for all n, then the sequence {a(n)} has infinitely many changes of sign.
Theorem.
Either the sequence {Re a(n)} has infinitely many sign changes or Re a(n) = 0 for all n. The same holds for the sequence {Im a(n)}. 相似文献
10.
We consider the problem of convergence of Fourier series when we make a change of variable. Under a certain reasonable hypothesis, we give a necessary and sufficient condition for a homeomorphism of the circle to transform absolutely convergent Fourier series into uniformly convergent Fourier series.
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E. D. Nursultanov 《Mathematical Notes》1998,63(2):205-214
In this paper we prove theorems on multiplicators of Fourier series inL
p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998. 相似文献
13.
Hiro-O Kitax 《Mathematische Nachrichten》1998,193(1):57-74
Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a0 < 1 such that then we have . 相似文献
14.
《Applied Mathematical Modelling》2014,38(21-22):5126-5148
This article applies the golden section search method (GSSM), simplex search method (SSM) and differential evolution (DE) for predicting the unknown Fourier number (Fo), Vernotte number (Ve) and non-dimensional solar heat flux (S1) in a flat-plate solar collector when subjected to a given temperature requirement. The required temperature field is calculated using an analytical forward method by considering Fourier and non-Fourier heat conduction, and using this, the inverse problem is solved to predict the Fo, Ve and S1 which are assumed to be the unknown parameters. The study reveals that the temperature field is highly sensitive to the Fo, thus even a small error in the temperature measurement can result in an unrealistic estimation of heating time of the collector. The present study is proposed to be useful in determining the time, the time lag and solar heat flux for controlled heating of an absorber plate within a stipulated time, which will be required to attain a prescribed/desired temperature distribution. Additionally, the study also shows that subjected to different time levels, the same temperature distribution is possible through different absorber plate materials. It has been observed from the present study that apart from SSM and DE, GSSM fails to estimate the unknown parameters at large value of Ve and small value of Fo, due to the associated fluctuation in the measured temperature field. The present study further discusses the computational performance of direct search method (e.g. GSSM and SSM) with that of the evolutionary method (DE) in terms of the maximum number of iteration and CPU time required to achieve the desired objective. 相似文献
15.
H. De Bie 《Mathematical Methods in the Applied Sciences》2012,35(18):2198-2228
In this review, we give an overview of several recent generalizations of the Fourier transform, related to either the Lie algebra or the Lie superalgebra . In the former case, one obtains scalar generalizations of the Fourier transform, including the fractional Fourier transform, the Dunkl transform, the radially deformed Fourier transform, and the super Fourier transform. In the latter case, one has to use the framework of Clifford analysis and arrives at the Clifford–Fourier transform and the radially deformed hypercomplex Fourier transform. A detailed exposition of all these transforms is given, with emphasis on aspects such as eigenfunctions and spectrum of the transform, characterization of the integral kernel, and connection with various special functions. Copyright © 2012 John Wiley & Sons, Ltd. 相似文献
16.
Gilbert Muraz Pawel Szeptycki 《Proceedings of the American Mathematical Society》1997,125(11):3275-3278
Translation invariant subspaces of the maximal domain of the Fourier transform (the amalgam of with ) are characterised: it turns out that in this case all measurable subsets of the dual space are sets of spectral synthesis.
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Varadharajan Muruganandam 《Mathematische Nachrichten》2008,281(11):1590-1603
We in this article, introduce a class of hypergroups called ultraspherical hypergroups and show that the Fourier space of an ultraspherical hypergroup forms a Banach algebra under pointwise product. These hypergroups need not be commutative and include for example double coset hypergroups. We also show that the structure space of this algebra equals the underlying hypergroup. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
A. A. Saakyan 《Mathematical Notes》2003,74(1-2):255-265
In this paper, we prove that for any compact set
there exists a homeomorphism of the closed interval
such that for an arbitrary function f the Fourier series of the function F(x,y) = f((x),(y)) converges uniformly on
simultaneously over rectangles, over spheres, and over triangles. 相似文献