| 分数阶小波变换 |
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| 引用本文： | 黄思齐.分数阶小波变换[J].测控技术,2009,28(2). |
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| 作者姓名： | 黄思齐 |
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| 作者单位： | 贵州省信息产业厅,信息化推进处,贵州,贵阳,550004 |
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| 摘 要： | 小波变换是对信号时域-频域(Fourier域)的多分辨率分析,也可看作是一种Fourier域伸缩带通滤波.分数阶Fourier变换是对传统Fourier变换的推广,对信号分析处理有更大的灵活性,为了将多分辨率分析理论推广到时域-广义频域(分数阶Fourier域),提出了一种分数阶小波变换,分析了分数阶小波变换在广义频域伸缩带通滤波特性,分析信号时的时域-广义频域平面的多分辨率分析网格划分.分数阶小波变换是传统小波变换的推广,在对原小波变换核作一定改动后增加了小波变换对信号处理的灵活性.可以看到,将分数阶小波变换的变换角度取为π/2,便得到与传统小波变换多分辨率分析理论完全一致的结果.理论分析和计算机仿真表明了所提理论的正确性和有效性.
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| 关 键 词： | 分数阶Fourier变换 小波变换 多分辨率分析 滤波 |
The Fractional Wavelet Transform |
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| HUANG Si-qi.The Fractional Wavelet Transform[J].Measurement & Control Technology,2009,28(2). |
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| Authors: | HUANG Si-qi |
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| Affiliation: | Promoting Information Technology Office;Guizhou Province Information Industry Deparment;Guiyang 550004;China |
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| Abstract: | The wavelet transform can be viewed as multi-resolution analysis of signals in the time-frequency(the Fourier domain) domain or as the linear filtering process with dilated band-pass filters of the Fourier domain.The fractional Fourier transform which is the generalized form of the well-known Fourier transform has more flexible properties for signal processing.Comparing with the primitive multi-resolution analysis of signals in the time-frequency domain,a multi-resolution analysis of signals in the time-fra... |
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| Keywords: | fractional Fourier transform wavelet transform multi-resolution analysis filters |
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