一维带限信号正则外推的快速算法  

A Fast Algorithm for The Regularization Extrapolation of 1 -D Band-Limited Signals

作　　者：肖庭延[1] 王彦飞[1] 

机构地区：[1]河北工业大学文理学院

出　　处：《信号处理》2001年第1期31-36,共6页Journal of Signal Processing

基　　金：河北省自然科学基金

摘　　要：本文给出用离散正则化方法进行一维带限信号外推的快速算法，其基本思想是将正则化方法与离散Ｆｏｕｒｉｅｒ变换（ＤＦＴ）结合起来，而正则参数的选取则基于偏差原理和作者提出的三阶收敛算法来实现。这样，可将计算量由原来的Ｏ（ ｎ３／３）量级减少到 Ｏ（ １２ｎ２）量级（当采样点 ｎ为偶数时）乃至Ｏ（１２／２ ）量级（当ｎ＝２*， ｐ为正整数时），分析和数值试验表明，新算法具有快速、稳定和抑制高频噪音干扰等优点。A fast algorithm for the extrapolation of 1-D band-limited signals by using discrete regularization method is presented in this paper. The new algorithm combines reguarizaiton mathod with DFT, in which the regularization parameter is based on discrepancy principle and determined numerically by a cubic convergence method posed by the authors. The computation amount can be reduced from O(n3/3)(n is sampling point) tO O(12n2) (n is even number) or even to O[(12/2)nlog2(n/2)] (if n=2p, p is integer number). Theoretical analysis and numerical simulation indicates that the new algorithm possesses the edvantages of high-speed, good stability and the inhibitation function against the noise of high frequencies.

关 键 词：快速算法 离散Fourier变换 带限信号外推 信号处理 

分 类 号：TN911.7[电子电信—通信与信息系统]