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
-
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.
-
Peltier R F and Levy Vehel J. Multifractional Brownianmotion: definition and preliminary results[R]. INRIAResearch Report, No. 2645, 1995.[2]Grossmann A and Morlet J. Decomposition of hardyfunctions into square integrable wavelets of constant shape[J].SIAM Journal on Mathematical Analysis.1984, 15(4):723-736[3]Mallat S A. Theory for multiresolution signal decomposition:the wavelet representation[J].IEEE Trans. on PatternAnalysis and Machine Intelligence.1989, 11(7):674-693[4]Percival D B and Walden A T. Wavelet Methods for TimeSeries Analysis[M]. Cambridge: Cambridge University Press,2000: 159-205.[5]Goncalves P and Abry P. Multiple-window wavelet transformand local scaling exponent estimation[A]. In Proceedings ofthe IEEE International Conference on Acoustics, Speech, andSignal Processing[C], Munich, Germany, 1997, 5: 3433-3436.[6]Wang Y, Cavanaugh J E, and Song C. Self-similarity indexestimation via wavelets for locally self-similar processes[J].Journal of Statistical Planning and Inference.2001, 99(11):91-110[7]Levy Vehel J. Signal enhancement based on Hder regularityanalysis[A]. In the IMA Volumes in Mathematics and ItsApplications[C], 2002, 132: 197-209.[8]Mallat S and Hwang W L. Singularity detection andprocessing with wavelets[J].IEEE Trans. on InformationTheory.1992, 38(2):617-643[9]Chan G and Wood A T A. Simulation of multifractionalBrownian motion[A]. In Proceedings in ComputationalStatistics 1998[C], Bristol, Great Britain, 1998: 233-238. -
计量
- 文章访问数: 3265
- HTML全文浏览量: 95
- PDF下载量: 710
- 被引次数: 0
下载:
