3阶B-样条小波的希尔伯特变换的消失矩  

On Vanishing Moments of Hilbert Transform of B-Spline Wavelets with Order Three

作　　者：杨秀竹 余波[1] YANG Xiuzhu;YU Bo(College of Science, China Three Gorges University, Yichang Hubei 443002, China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《西南师范大学学报（自然科学版）》2021年第12期31-36,共6页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11301296).

摘　　要：本文研究了3阶B样条小波的希尔伯特变换的消失矩.首先计算了3阶B样条小波的分段函数形式的表达式,并且给出了其图像.3阶B样条小波具有紧支撑性、反对称性以及良好的光滑性.在此基础上,结合希尔伯特变换的定义计算了3阶B样条小波的希尔伯特变换,给出了其图像.3阶B样条小波经过希尔伯特变换后不再具有紧支撑性,反对称性也变为对称性,但保持了良好的光滑性.最后利用消失矩的定义计算了3阶B样条小波的希尔伯特变换的消失矩.结果表明,3阶B样条小波的希尔伯特变换虽然不再是一个有限支撑的函数,但它比3阶B样条小波本身具有更高的消失矩,这一发现对构成希尔伯特变换对的小波的设计具有启发意义.The vanishing moments of Hilbert transform of B-spline wavelets with order three will be studied in this paper.In order to achieve this goal,we first calculate the piecewise function expression of B-spline wavelet with order three,and give its image.The B-spline wavelets with order three are compactly supported,anti-symmetric and smooth.On this basis,combined with the definition of Hilbert transform,the Hilbert transform of B-spline wavelets with order three is calculated,and its image is given.After Hilbert transform,B-spline wavelets with order three no longer have compact support,and their anti-symmetry becomes symmetric,but they keep good smoothness.Finally,we use the definition of vanishing moment to calculate the vanishing moment of Hilbert transform of B-spline wavelets of order three.The results show that the Hilbert transform of B-spline wavelets with order three is no longer a function with limited support,but it has higher vanishing moment than the B-spline wavelets with order three itself.This discovery is instructive for the design of wavelets that constitute Hilbert transform pairs.

关 键 词：B样条小波 消失矩 希尔伯特变换 

分 类 号：O241.86[理学—计算数学]