The extrapolation of a band-limited signal is in terms of its finite known segment in the time interval $[-T,T]$ for T > 0 to determine the unknown part of the signal. Some of the singular values of the operator of the reconstruction equation are close to 1 while the rest are close to zero, and if T is small, more singular values are close to zero. In this paper, we theoretically improve the posedness of the extrapolation of a band-limited signal by using a reweighting method to improve the distribution properties of all eigenvalues in infinite dimensions and accordingly propose a reweighted Landweber scheme. In the implementation, a high accuracy numerical method of the operator of the equation for reconstruction is proposed to reduce the truncated errors of the reconstruction equation and thus the accumulative errors of the reweighting method. Numerical experiments validate the proposed method. Compared with our previous work and existing works, effective reconstructions are obtained with a much smaller T.

限带信号的外推是根据时间间隔内的有限已知段 $[-Ť，Ť]$当T  > 0时，确定信号的未知部分。重建方程算子的一些奇异值接近1，而其余则接近零，如果T较小，更奇异的值接近零。在本文中，我们在理论上通过使用重加权方法来改善带限信号的外推性，从而改善了无限维上所有特征值的分布特性，并据此提出了一种重加权的Landweber方案。在实现中，提出了一种用于重构方程算子的高精度数值方法，以减少重构方程的截断误差，从而减少了加权方法的累积误差。数值实验验证了该方法的有效性。与我们以前的工作和现有工作相比，使用小得多的T可获得有效的重构。