确定分形函数的局部奇异性指数及其谱  

Determining the Local Singularity Exponents and Spectrum of the Fractal Function

作　　者：王兆瑞[1] 吕善伟[1] 中村武恒[2] 

机构地区：[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,日本京都615-8510

出　　处：《电子与信息学报》2008年第2期290-292,共3页Journal of Electronics & Information Technology

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。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.

关 键 词：奇异性谱 局部Holder指数 小波变换 

分 类 号：TN911.7[电子电信—通信与信息系统]