分数阶小波变换的性质  

Properties of the Fractional Wavelet Transform

作　　者：黄思齐[1] 姚加明 许兴武 

机构地区：[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

出　　处：《测控技术》2009年第4期15-17,共3页Measurement & Control Technology

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。The wavelet transform can be viewed as multi-resolution analysis of signals in the time-frequency （ the Fourier domain） domain or as the linear time-variant filtering process with dilated band-pass filters. Comparing with the primitive multi-resolution analysis of signals in the time-frequency 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 well-known wavelet transform, develops multi-resolution analysis of signals in the time-fractional Fourier domain. The properties of the fractional wavelet are analyzed. Conclusions verify that the fractional wavelet transform can be viewed as the linear time-variant filtering process with dilated band-pass filters of the fractional Fourier domain and there are orthogonal bases of fractional wavelets with limitable condition associated with the fractional wavelet transform.

关 键 词：小波变换 多分辨率分析 分数阶FOURIER变换 滤波器 

分 类 号：TN957.5[电子电信—信号与信息处理] TN911.7[电子电信—信息与通信工程]