A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited...A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Orthogonal Functions (EOF’s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure.展开更多
In this paper, we present some new algorithms to reconstruct multivariate band-limited functionsfrom irregular sampled values, which allow more arbitrary sampling points and lower sampling densities thanknown results.
In this work,a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed.Te proposed method is based on a novel numerical scheme for the rapid calculat...In this work,a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed.Te proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives,exhibiting high accuracy,with error magnitude of O(10^(−100))or less.A variety of integrated radial basis functions are utilized for the solution,as well as variable precision arithmetic for the calculations.Multiple alterations in the function’s direction,with no curvature or periodicity information specifed,are efciently foreseen.Interestingly,the proposed procedure can be extended in multiple dimensions.Te attained extrapolation spans are greater than two times the given domain length.Te signifcance of the approximation errors is comprehensively analyzed and reported,for 5832 test cases.展开更多
文摘A one-step band-limited extrapolation procedure is systematically developed under an a priori assumption of bandwidth. The rationale of the proposed scheme is to expand the known signal segment based on a band-limited basis function set and then to generate a set of Empirical Orthogonal Functions (EOF’s) adaptively from the sample values of the band-limited function set. Simulation results indicate that, in addi- tion to the attractive adaptive feature, this scheme also appears to guarantee a smooth result for inexact data, thus suggesting the robustness of the proposed procedure.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos. 10171050, 10201014) the Mathematical Tianyuan Foundation(Grant No. TY10126007) the Research Fund for the Doctoral Program of Higher Education, and the Liuhui Cen
文摘In this paper, we present some new algorithms to reconstruct multivariate band-limited functionsfrom irregular sampled values, which allow more arbitrary sampling points and lower sampling densities thanknown results.
文摘In this work,a numerical solution for the extrapolation problem of a discrete set of n values of an unknown analytic function is developed.Te proposed method is based on a novel numerical scheme for the rapid calculation of higher order derivatives,exhibiting high accuracy,with error magnitude of O(10^(−100))or less.A variety of integrated radial basis functions are utilized for the solution,as well as variable precision arithmetic for the calculations.Multiple alterations in the function’s direction,with no curvature or periodicity information specifed,are efciently foreseen.Interestingly,the proposed procedure can be extended in multiple dimensions.Te attained extrapolation spans are greater than two times the given domain length.Te signifcance of the approximation errors is comprehensively analyzed and reported,for 5832 test cases.
