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

摘要

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. 【Keywords】Fractional Gaussian noise (fGn);Multifractional Gaussian noise (mGn);Multifractional Brownian motion (mBm);Fractional-order signal processing (FOSP);Variable-order fractional operator;Multifractional a-stable noise