Nonlinear Approximation by Trigonometric Sums
نویسندگان
چکیده
منابع مشابه
Nonlinear approximation by sums of nonincreasing exponentials
Many applications in electrical engineering, signal processing, and mathematical physics lead to following approximation problem: Let h be a short linear combination of nonincreasing exponentials with complex exponents. Determine all exponents, all coefficients, and the number of summands from finitely many equispaced sampled data of h. This is a nonlinear inverse problem. This paper is an exte...
متن کاملApproximation By Trigonometric Polynomials
These notes are prepared as lecture notes exclusively for the participants of this conference only. Any reproduction in any media, or any use for any other purpose of any part of this manuscript, without an expressed written consent of the author is unlawful.thorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notation thereon. The views and conc...
متن کاملNonlinear Approximation by Sums of Exponentials and Translates
In this paper, we discuss the numerical solution of two nonlinear approximation problems. Many applications in electrical engineering, signal processing, and mathematical physics lead to the following problem. Let h be a linear combination of exponentials with real frequencies. Determine all frequencies, all coefficients, and the number of summands if finitely many perturbed, uniformly sampled ...
متن کاملNonlinear Approximation of Functions by Sums of Wave Packets∗
We consider the problem of approximating functions by sums of wave packets. Our objective is to find sparse decompositions of image functions, over a finite range of scales. We also address the naturally connected task of approximating the wavefront set, computationally. We formulate the problem in terms of Hankel operators, Hankel matrices and their low-rank approximations, and develop an alge...
متن کاملOn Some Trigonometric Power Sums
In contrast to Fourier series, these finite power sums are over the angles equally dividing the upper-half plane. Moreover, these beautiful and somewhat surprising sums often arise in analysis. In this note, we extend the above results to the power sums as shown in identities (17), (19), (25), (26), (32), (33), (34), (35), and (36) and in the appendix. The method is based on the generating func...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 1995
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-001-4021-8