一种有效的分段光滑信号逼近方法

doi:10.3969/j.issn.0372-2112.2016.08.033

电子学报 ›› 2016, Vol. 44 ›› Issue (8): 2004-2008.DOI: 10.3969/j.issn.0372-2112.2016.08.033

一种有效的分段光滑信号逼近方法

陈伟

江南大学数字媒体学院, 江苏无锡 214122

收稿日期:2015-06-15 修回日期:2015-12-28 出版日期:2016-08-25 发布日期:2016-08-25
作者简介:陈伟男,1986年1月出生于江苏省宝应县.2013年获得澳门科技大学理学博士学位,现为江南大学数字媒体学院讲师,主要研究兴趣为小波分析和计算机图形学.E-mail:wchen_jdsm@163.com
基金资助:
国家自然科学基金（No.61170320，No.61272026）；浙江大学CAD&CG国家重点实验室开放课题（No.A1513，No.A1609）；中央高校基本科研业务费（No.JUSRP11416）

An Efficient Approximation Method for Piecewise Smooth Signal

CHEN Wei

School of Digital Media, Jiangnan University, Wuxi, Jiangsu 214122, China

Received:2015-06-15 Revised:2015-12-28 Online:2016-08-25 Published:2016-08-25

摘要/Abstract

摘要： 传统的Fourier变换，连续小波变换等方法在逼近具有分段光滑特性的非连续信号时，因Gibbs现象的干扰会产生比较大的误差.本文提出了一种有效的分段光滑信号逼近方法.首先根据给定信号的分段点位置，构造一组标准正交分段多项式系，该函数系具有正交性，收敛性及再生性.然后将信号在该函数系下进行正交分解及重构，即可得到该信号的最佳平方逼近结果.数值实验表明，本文方法比传统的正交基具有更好的逼近结果.

关键词: 分段光滑信号, 逼近, Gibbs现象, 正交表达

Abstract: The truncating Fourier and continue wavelet representation of a discontinuous piecewise smooth signal will introduce an unneglectable error which was named as the Gibbs phenomenon. In this paper, we proposed an effective piecewise smooth signal approximation method. Firstly, a set of normal orthogonal piecewise polynomials was constructed according to the given positions of breaking points, and it has the properties of orthogonality, convergence and reproduction. Then the signal was orthogonal decomposed under this basis and the best square approximation result could be obtained using reconstruction. The numerical experiments show that our method have the higher accuracy approximation results than the other basis.

Key words: piecewise smooth signal, approximation, Gibbs phenomenon, orthogonal representation

中图分类号:

TP302.4

陈伟. 一种有效的分段光滑信号逼近方法[J]. 电子学报, 2016, 44(8): 2004-2008.

CHEN Wei. An Efficient Approximation Method for Piecewise Smooth Signal[J]. Acta Electronica Sinica, 2016, 44(8): 2004-2008.

参考文献

[1] Harr A.Zur theorei der orthogonalen funkionen systeme[J].Mathematische Annalen,1910,69(3):331-371.
[2] Walsh J L.A closed of normal orthogonal functions[J].American Journal of Mathematics,1923,45(1):5-24.
[3] Feng Y Y,Qi D X.A sequence of piecewise orthogonal polynomials[J].SIAM Journal on Mathematical Analysis,1984,15(4):834-844.
[4] Micchelli C,Xu Y S.Using the matrix refinement equation for the construction of wavelets on invariant sets[J].Applied and Computational Harmonic Analysis,1994,1(4):191-401.
[5] Alpert B K.A class of bases in L² for the spares representation of integral operators[J].SIMA Journal on Mathematical Analysis,1993,24(1):246-262.
[6] Beam R M,Warming R F.Multiresolution analysis and supercompact multiwavelets[J].SIMA Journal on Scientific Computing,2002,22(4):1238-1268.
[7] Song R X,Ma H,Wang T J,et al.Complete orthogonal V-system and its applications[J].Communications on Pure and Applied Analysis,2007,6(3):853-971.
[8] Huang C,Yang L H,Qi D X.A new class of multi-wavelet bases:V-system[J].Acta Mathematica Sinica,2012,28(1):105-120.
[9] 齐东旭,陶尘钧,宋瑞霞,等.基于正交完备U-系统的参数曲线图组表达[J].计算机学报,2006,29(5):778-785.Qi D X,Tao C J,Song R X,et al.Representation for a group of parametric curves based on the orthogonal complete U-System[J].Chinese Journal of Computers,2006,29(5):778-485.(in Chinese)
[10] 蔡占川,孙伟,齐东旭.基于正交完备U-系统的图形分类与识别方法[J].软件学报,2006,17(Supplement):21-27.Cai Z C,Sun W,Qi D X.A Classification and recognition method for planar figures based on complete orthogonal U-System[J].Journal of Software,2006,17(Supplement):21-27.(in Chinese)
[11] 熊刚强,齐东旭,郭芬红.一类完备的正交分段多项式函数系及其应用[J].中国科学:信息科学,2012,42(1):70-82.Xiong G Q,Qi D X,Guo F H.A class of orthonormal complete piecewise polynomial systems and applications thereof[J].Scientia Sinica Informationis,2012,42(1):70-82.(in Chinese)
[12] Song R X,Zhao Z X,Wang X C.An application of the V-system to the clustering of cherno faces[J].Computers and Graphics,2010,34(5):529-536.
[13] Song R X,Yao D X,Wang X C,et al.Retrieval method for 3D object group based on V-system[J].Journal of Advanced Mechanical Design,System and Manufacturing,2012,6(3):340-353.

[1]	黄丙耀, 檀结庆. 一类混合型三重细分法[J]. 电子学报, 2021, 49(1): 90-98.
[2]	孙悦, 王传伟, 康龙飞, 叶超, 张信. 基于CORDIC的精确快速幅相解算方法[J]. 电子学报, 2018, 46(12): 2978-2984.
[3]	贾正荣, 卢发兴, 吴玲. 基于函数逼近的未来空域窗瞄准点配置方法[J]. 电子学报, 2017, 45(8): 2031-2037.
[4]	董文强, 王贵君. 基于调控参数建模的混合模糊系统的逼近分析[J]. 电子学报, 2017, 45(5): 1158-1164.
[5]	伊文坛, 田亚, 陈少真. 减缩轮PRIDE算法的线性分析[J]. 电子学报, 2017, 45(2): 468-476.
[6]	冯翔, 陈志坤, 李风从, 赵宜楠. 基于松弛交替投影的MIMO雷达相位编码波形设计[J]. 电子学报, 2016, 44(12): 2981-2988.
[7]	汪正锋, 宁宁, 吴霜毅, 杜翎, 蒋旻, 闫小艳, 王伟. 一种基于电压窗口技术的超低功耗SAR ADC[J]. 电子学报, 2016, 44(1): 211-215.
[8]	王健, 戚文峰, 郑群雄. 模m加法的一类线性逼近关系研究[J]. 电子学报, 2015, 43(11): 2194-2199.
[9]	陶玉杰, 王宏志, 王贵君. Kp-积分模意义下广义Mamdani模糊系统的逼近性能及其实现[J]. 电子学报, 2015, 43(11): 2284-2291.
[10]	袁学海, 李洪兴, 杨雪. 基于模糊变换的模糊系统和模糊推理建模法[J]. 电子学报, 2013, 41(4): 674-680.
[11]	李风从, 赵宜楠, 乔晓林. 零自相关区相位编码波形设计[J]. 电子学报, 2013, 41(12): 2499-2502.
[12]	刘晶;王映辉;刘刚;段敬红. 基于几何方向的图像压缩算法[J]. 电子学报, 2011, 39(7): 1693-1697.
[13]	袁学海;李洪兴;孙凯彪. 基于参数单点模糊化方法的模糊系统及其逼近能力[J]. 电子学报, 2011, 39(10): 2372-2377.
[14]	王新;黄志祥;吴先良. 基于高阶抛物线方程求解目标雷达散射截面[J]. 电子学报, 2010, 38(9): 2118-2121.
[15]	徐小来;雷英杰;谢文彪. 基于UKF的自组织直觉模糊神经网络[J]. 电子学报, 2010, 38(3): 638-645.

一种有效的分段光滑信号逼近方法

An Efficient Approximation Method for Piecewise Smooth Signal

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics