| 黄思齐1， 姚加明2， 许兴武3 |
（1. 贵州省信息产业厅 信息化推进处，贵州 贵阳550004； 2. 江苏武进液压启闭机有限公司,江苏 常州213131; 3. 南京市三汊河河口闸管理处,江苏 南京210036） |
 摘要：小波变换是对信号时域－频域（Fourier域）的多分辨率分析，是一种线性时不变伸缩带通滤波。分数阶小波变换将小波变换的多分辨率分析理论推广到时域－广义频域(分数阶Fourier域)，对信号分析处理有更大的灵活性。分析了分数阶小波变换的线性时变特性、存在正交分数阶小波的条件、分数阶Fourier域传递函数，以及分数阶小波变换在分数阶Fourier域的伸缩带通滤波。 |
| 关键词：小波变换;多分辨率分析;分数阶Fourier变换;滤波器 |
| 中图分类号：TN957.5；TN911.7文献标识码：A文章编号：1000-8829(2009)04-0015-03 |
| Properties of the Fractional Wavelet Transform |
| HUANG Siqi1，YAO Jiaming2， XU Xingwu3 |
| (1. Promoting Information Technology Office,Guizhou Province Information Industry Deparment,Guiyang 550004,China；2. Jiangsu Wujin Hydraulic Hoist Co.,Ltd.,Changzhou 213131,China;3. Gateway Sancha River Estuary Management Office，Nanjing 210036,China) |
| Abstract：The wavelet transform can be viewed as multiresolution analysis of signals in the timefrequency (the Fourier domain) domain or as the linear timevariant filtering process with dilated bandpass filters.Comparing with the primitive multiresolution analysis of signals in the timefrequency domain,the fractional wavelet transform (FRWT),a generalization of the wavelet transform,which is a flexible method for the signal processing with trivial complexity compared with the wellknown wavelet transform,develops multiresolution analysis of signals in the timefractional Fourier domain.The properties of the fractional wavelet are analyzed.Conclusions verify that the fractional wavelet transform can be viewed as the linear timevariant filtering process with dilated bandpass filters of the fractional Fourier domain and there are orthogonal bases of fractional wavelets with limitable condition associated with the fractional wavelet transform. |
| Key words：wavelet transform;multiresolution analysis;fractional Fourier transform;filters |
|
|
