| 一种改进的第2代小波变换算法及应用 |
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| 引用本文： | 段晨东,姜洪开,何正嘉.一种改进的第2代小波变换算法及应用[J].西安交通大学学报,2004,38(1):47-50. |
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| 作者姓名： | 段晨东 姜洪开 何正嘉 |
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| 作者单位： | 西安交通大学机械工程学院,710049,西安 |
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| 基金项目： | 国家自然科学基金资助项目(50175087)，国家"十五"科技攻关计划重点项目(2001BA204B05). |
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| 摘 要： | 为了获得基于分析数据特征的小波函数，将第2代小波变换插值细分方法与最优估计理论相结合，提出了一种改进的第2代小波变换算法，在设计预测系数时，以小波分解的细节信号的平方和最小为目标函数，使预测满足一定的消失矩，通过最小二乘法确定预测系数，使预测系数能够反映分析数据的特征，采用最优插值估计的第2代小波变换分解及重构算法的降噪效果优于其他类型的小波，因此较理想地提高了滚动轴承振动信号的信噪比。
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| 关 键 词： | 第2代小波变换 插值细分 预测系数 最优估计 |
| 文章编号： | 0253-987X(2004)01-0047-04 |
| 修稿时间： | 2003年5月23日 |
Improved Algorithm for Second Generation Wavelet Transform and Its Application |
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| Duan Chendong,Jiang Hongkai,He Zhengjia.Improved Algorithm for Second Generation Wavelet Transform and Its Application[J].Journal of Xi'an Jiaotong University,2004,38(1):47-50. |
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| Authors: | Duan Chendong Jiang Hongkai He Zhengjia |
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| Abstract: | In order to obtain a wavelet function based on the characteristics of a set of data, an improved algorithm for second generation wavelet transform (SGWT) is proposed by adopting the interpolating subdivision scheme and optimum estimation theorem. For designing predicting coefficients of SGWT, the sum of squared detail components are taken as an objective function, and the coefficients are solved by least square method with constraint of vanishing moment number for predicting. These coefficients can represent features of the given data. An optimum interpolating estimation algorithm of SGWT decomposition and reconstruction is also described. The proposed method is proved to be more effective than other wavelets for signal de-noising. It greatly improves signal noise ratio of ball bearing vibration signal in an application. |
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| Keywords: | second generation wavelet transform (SGWT) interpolating subdivision predicting coefficient optimum estimation |
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