确定分形函数的局部奇异性指数及其谱
doi: 10.3724/SP.J.1146.2006.01178
Determining the Local Singularity Exponents and Spectrum of the Fractal Function
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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。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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