依照本文提出的带宽有限信号外推的算子D逼近法,利用Taylor展开式对逆算子1/D作逼近,揭示了传统的Papoulis方法收敛慢的本质原因。而采用文中提出的另一新的外推方法——相应于用Tchebycheff展开式逼近逆算子1/D,则可获得快得多的收敛速度。 According to the operator D approximation method of extrapolating bandwidth limited signals proposed in this paper, Taylor’s expansion method is used to approximate the inverse operator 1 / D, revealing the slowness of convergence of the traditional Papoulis method. However, another new extrapolation method proposed in this paper is adopted - corresponding to the approximation of inverse operator 1 / D by Tchebycheff expansion, a much faster convergence rate can be obtained.