Applies to version: 1.1.0

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BRUCE2018_FFGN - Fast (exact) fractional Gaussian noise and Brownian motion generator


y = bruce2018_ffgn(N, tdres, Hinput, noiseType, mu, sigma)

Input parameters

N is the length of the output sequence.
tdres is the time resolution (1/sampling rate)
is the "Hurst" index of the resultant noise (0 < H <= 2)
For 0 < H <= 1,the output will be fractional Gaussian noise with Hurst index H. For 1 < H <= 2, the output will be fractional Brownian motion with Hurst index H-1. Either way, the power spectral density of the output will be nominally proportional to 1/f^(2H-1).
noiseType is 0 for fixed fGn noise and 1 for variable fGn
mu is the mean of the noise. [default = 0]
sigma is the standard deviation of the noise. [default = 1]

Output parameters

y a sequence of fractional Gaussian noise with a mean of zero and a standard deviation of one or fractional Brownian motion derived from such fractional Gaussian noise.


returns a vector containing a sequence of fractional Gaussian noise or fractional Brownian motion. The generation process uses an FFT which makes it very fast.


R. Davies and D. Harte. Tests for hurst effect. Biometrika, 74(1):95 -- 101, 1987.

J. Beran. Statistics for long-memory processes, volume 61. CRC Press, 1994.

J. Bardet. Statistical study of the wavelet analysis of fractional brownian motion. Information Theory, IEEE Transactions on, 48(4):991--999, 2002.