Synthesis of multifractional Gaussian noises based on variable-order fractional operators

Authors:
Hu Sheng;Hongguang Sun;YangQuan Chen;TianShuang Qiu
Affiliations:
Department of Electronic Engineering, Dalian University of Technology, Dalian 116024, China and CSOIS, Electrical and Computer Engineering Department, Utah State University, Logan 84322, USA;CSOIS, Electrical and Computer Engineering Department, Utah State University, Logan 84322, USA and Institute of Soft Matter Mechanics, Department of Engineering Mechanics, Hohai University, 210098 ...;CSOIS, Electrical and Computer Engineering Department, Utah State University, Logan 84322, USA;Department of Electronic Engineering, Dalian University of Technology, Dalian 116024, China
Venue:
Signal Processing
Year:
2011

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Abstract

In this paper, a synthesis method, which is based on variable-order fractional operators, for multifractional Gaussian noises (mGn) is proposed by studying the relationship of white Gaussian noise (wGn), mGn, and multifractional Brownian motion (mBm). Furthermore, a synthesis method for multifractional @a@?stable processes, the generalization of mGn, is proposed in order to more accurately characterize the processes with local scaling characteristics and heavy tailed distributions. Synthetic examples of mGn and multifractional @a@?stable noises are provided for illustration.