一种带限信号重建和外推的方法

A New Algorithm for Reconstructing and Extrapolating band-limited Signals Using Fourier Transform and Regularization Methods

讨论一种新的高频重建的数值方法。此方法包括三步:首先将问题用傅立叶变换到频域;其次,用Tikhonov正则化方法求问题的正则解;最后用傅立叶反变换变回时域。它能充分利用卷积型积分方程的特性,计算复杂度低。文中给出算法,证明收敛性;还给出计算机实验结果。

In this paper, a new numerical method for reconstructing and extrapolating band - limited signal is described. This methed consists of three steps, firstly, transform inital problem into the domain of frequency; secondly, solve the problems in domain of frequency by Tikhohov regularization method; thirdly, turn the solution into the domain of time. This algorithm can make the best use of the characters of the integral equations of convolution type, and the computational complexity is also lower. In this paper,the algorithm,proof of the convergence and some results of computer experiment are presented.