Fast and Exact Synthesis for 1-D Fractional Brownian Motion and Fractional Gaussian Noises

Emmanuel Perrin , Rachid Harba (1) , Rachid Jennane (1) , Ileana Iribarren (2)

1 IRAUS - Département Images, Robotique, Automatique et Signal [Orléans]
2 Escuela de Matematicas [Caracas]

In this letter, it is shown that fast and exact fractional Brownian motion (fBm) and fractional Gaussian noise (fGn) signals can be synthesized by the circulant embedding method (CEM). CEM consists in embedding the NxN covariance matrix of the stationary fGn process in a larger 2Mx2M circulant matrix such that M>=N-1. CEM is exact, since second-order statistics of the generated data are those of the Gaussian fGn. CEM is fast, since the optimal case M = N-1 can be reached. Fast and exact fBm sequences can be easily recovered from fGn ones.

Mots clés: Fast algorithms; fractional Brownian motion; fractional Gaussian noises; synthesis

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Emmanuel Perrin, Rachid Harba, Rachid Jennane, Ileana Iribarren. Fast and Exact Synthesis for 1-D Fractional Brownian Motion and Fractional Gaussian Noises. IEEE Signal Processing Letters, 2002, 9 (11), pp.382-384. ⟨hal-00768776⟩