## 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
Full Text:

### References:

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