一类高振荡Hilbert变换的计算

On the Evaluation of Hilbert Transform of Oscillatory Functions

Hilbert变换在信号处理与医学图像处理中都有着广泛的应用,但是对于一般的含有高振荡因子且在积分区间中包含奇异值的Hilbert变换往往处理起来较为困难,本文提出了一种基于等距节点插值的高效计算方法。

Hilbert transform is widely used in signal processing and medical imaging processing,but it is generally difficult to deal with the integral which include the highly oscillstory function and a singular value in the Hilbert transform, So this paper presents a method which interpolate in the equispaoed nodes. And then we give a numerical example to verify the efficiency of this method.