平移不变空间中信号的min-max插值重建方法

摘要

Signal reconstruction from finitely number of non-uniform samples on a interval is considered in the frame of shift invariant space. We derive a new interpolation method that is approximately optimal at min-max criterion for signals in a shift invariant space,and can regain Yen's interpolator for band-limited signals. Based on the derived interpolator, we also propose an effective non-iterative algorithm for min-max signal reconstruction. Some numerical examples are given to show the effectiveness of the new method.%在一般平移不变子空间框架下讨论信号的有限非一致采样重建的问题.基于信号的子空间表示,本文给出一般信号在min-max插值准则下的最优插值方法以及相应的非迭代算法.该方法可以导出著名带限信号的Yen插值.数值实验表明所给方法能十分有效地重建信号.