| 确定分形函数的局部奇异性指数及其谱 |
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| 引用本文： | 王兆瑞,吕善伟,中村武恒.确定分形函数的局部奇异性指数及其谱[J].电子与信息学报,2008,30(2):290-292. |
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| 作者姓名： | 王兆瑞 吕善伟 中村武恒 |
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| 作者单位： | 1. 北京航空航天大学电子信息工程学院,北京,100083
2. 京都大学电子工程系,京都,615-8510,日本 |
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| 摘 要： | 基于配分函数的多分形形式仅仅提供了信号奇异性指数的全局描述，并没有给出局部信息，然而在实际应用中，揭示出信号的局部奇异性信息往往更具有重要性。该文提出了一种确定信号局部奇异性指数的新算法，构造了一种类似于奇异性谱的直方图，并用来描述信号奇异性的全局统计分布。数字试验验证了该算法的有效性。
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| 关 键 词： | 奇异性谱 局部Hlder指数 小波变换 |
| 文章编号： | 1009-5896（2008）02-0290-03 |
| 收稿时间： | 2006-08-09 |
| 修稿时间： | 2007-01-11 |
Determining the Local Singularity Exponents and Spectrum of the Fractal Function |
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| Wang Zhao-rui,Lü Shan-wei,Nakamura Taketsune.Determining the Local Singularity Exponents and Spectrum of the Fractal Function[J].Journal of Electronics & Information Technology,2008,30(2):290-292. |
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| Authors: | Wang Zhao-rui Lü Shan-wei Nakamura Taketsune |
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| Affiliation: | School of Electronic and Information Engineering, Beihang University, Beijing 100083, China;Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan |
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| Abstract: | Traditional partition function-based multifractal formalism provides only global estimates of singularity exponents, no local information is offered. However, it is more important to recover the local singularity. A novel algorithm for determining the local singularity exponents is proposed, which provides the local scaling information of interest, whilst a singularity-spectrum-like histogram is constructed to describe the global statistical distribution of the local singularity strengths. The validity is verified by numerical experiment. |
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| Keywords: | Singularity spectrum Local Holder exponents Wavelet transform |
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