一种基于小波变换的多分形布朗运动合成算法  

Synthesis algorithm of multifractional Brownian motion with wavelet

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]京都大学电气系

出　　处：《北京航空航天大学学报》2007年第12期1417-1419,1456,共4页Journal of Beijing University of Aeronautics and Astronautics

摘　　要：为了更有效地描述点状奇异性指数沿样本路径变化的信号,利用多分形的概念,在基于离散小波变换技术的基础上,提出了一种合成多分形布朗运动的新算法.该算法通过控制高斯白噪声的小波系数权来获得期望的信号局部正则性,而合成过程的收敛性由收敛因子保证.通过与基于Durbin-Levinson和轮换矩阵嵌入技术算法的比较以及数字仿真试验,表明提出的算法不仅计算复杂度低,而且适用于生成非高斯的、自协方差函数事先未知的多分形过程.In practice, the signals being analyzed are often very far from regular or smooth, and these irregular signals usually have many non-differentiable points, even nowhere differentiable. To describe the signal whose pointwise singularity varies along the sample path, in terms of the concept of multifractal, a new algorithm based on discrete wavelet transform for synthesis of multifractional Brownian motion was proposed. The desired local regularity of the multifractional process was obtained by controlling the weights of the wavelet expansion of the Gaussian white noise. The convergence of the synthesized process was controlled by an experi- mental factor. Compared with both Durbin-Levinson model and circulant matrix embedding model, this algo- rithm is not only time saving, but also appropriate for generating the multifractional process that is non-Gaussian and autocovariance function unknown in advance. The validity and rationality were verified by numerical experiments.

关 键 词：小波变换 奇异性 多分形布朗运动 

分 类 号：TN911.7[电子电信—通信与信息系统]