Multifractal Spectrum and Calculation
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摘要: 多重分形理论是进行信号奇异性处理的有用工具,由于只有少数集合的多重分形谱可以有解析表达式,多重分形谱的计算是其中重要而又较难处理的问题.简要介绍了多重分形理论的一种形式体系,提出了一种采用动态链表来进行多重分形谱计算的方法,大幅度地降低了对存储器容量的要求.用所提出的方法对康托集进行了计算,计算结果与理论结果相符,表明了算法的有效性.Abstract: Multifractal theory is an effective tool for the singularity processing of signal, but only a few special sets have analytic multifractal spectrum expression. The calculation of multifractal spectrum is important and difficult. This paper introduces one of the formal system of multifractal theory in brief and presents an approach to calculate the multifractal spectrum of general sets. The approach makes use of the dynamic link data structure and decreases greatly the demand for memory. By means of the approach , the multifractal spectrum of Cantor set is calculated. The result is in accordance with the theory analysis and shows that the presented algorithm is valid.
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Key words:
- signal processing /
- spectral analysis /
- singularity /
- multifractal /
- multifractal spectrum
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