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Synthesis of multifractional Gaussian noises based on variable-order fractional operators. (English) Zbl 1213.94049

Summary: 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 \(\alpha \)-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 \(\alpha \)-stable noises are provided for illustration.

MSC:

94A12 Signal theory (characterization, reconstruction, filtering, etc.)

Software:

fractPC; Matlab; longmemo
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