模型分形和多重分形信号的多重分形分析

IF 0.2 Q4 ENGINEERING, ELECTRICAL & ELECTRONIC Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia Pub Date : 2022-12-30 DOI:10.30837/rt.2022.4.211.05
O. Lazorenko, A. A. Onishchenko, L. Chernogor
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引用次数: 0

摘要

现代分形射电物理学的一个热门方向是对各种来源的信号和过程进行多重分形分析。提出了一套时域单分形和多重分形信号和过程的确定性和随机模型。介绍了多重分形信号的新特征,即多重分形谱函数的不对称系数、多重分形谱的相对宽度和多重分形支撑的维数,并通过实例说明了使用它们的必要性。利用小波变换模极大值法和多重分形去趋势波动分析法,对模型信号进行了详细的多重分形分析。建立了单分形、多重分形和非分形信号多重分形分析的特点,并对从业者提出了相应的建议。已经开发了方便的格式来呈现分析结果。研究发现,在多重分形信号向单分形状态过渡的过程中,物理分形的多重分形谱函数不会像数学分形在理论上应该发生的那样坍缩成一个点。提出了多重分形特征的阈值,它是单分形出现的指标。研究表明,对非分形信号进行多重分形分析,会产生多重分形特征值异常的多重分形谱。修正函数法适用于信号和过程的多重分形分析方法。结果表明,利用该方法可以将得到的广义赫斯特指数的估计与被分析信号Hölder指数的真实已知值的偏差从5 - 90%减小到3 - 8%。
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Multifractal analysis of model fractal and multifractal signals
One of the topical directions of modern fractal radio physics is the multifractal analysis of signals and processes of various origins. A set of deterministic and stochastic models of monofractal and multifractal signals and processes in the time domain is proposed. New multifractal signal characteristics, namely, the coefficient of asymmetry of the multifractal spectrum function, the relative width of the multifractal spectrum and the dimension of the multifractal support, are introduced, the necessity of their use is demonstrated on examples. Using Wavelet Transform Modulus Maxima Method and Multi-Fractal Detrended Fluctuation Analysis Method, a detailed multifractal analysis of model signals is performed. The features of multifractal analysis of monofractal, multifractal and non-fractal signals are established, the appropriate recommendations for practitioners are formulated. Convenient formats for presenting analysis results have been developed. It was found that during the transition of the multifractal signal to the monofractal regime, the function of the multifractal spectrum of the physical fractal does not collapse into a point, as it should happen in theory for a mathematical fractal. Threshold values of multifractal characteristics, which are indicators of the appearance of the monofractal, are proposed. It has been shown that multifractal analysis of non-fractal signals leads to the appearance of multifractal spectra with anomalous values of multifractal characteristics. The correction function method is modified for the methods of multifractal analysis of signals and processes. It is proved that its usage makes it possible to reduce the deviation of the obtained estimate of the generalized Hurst exponent from the true known value of the Hölder exponent of the analyzed signal from 5 – 90% to 3 – 8%.
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Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia
Visnyk NTUU KPI Seriia-Radiotekhnika Radioaparatobuduvannia ENGINEERING, ELECTRICAL & ELECTRONIC-
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