Applies to version: 1.1.0

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ZILANY2014_FFGN - Fast (exact) fractional Gaussian noise and Brownian motion generator


Y = zilany2014_ffGn(N, tdres, Hinput)

Input parameters

N is the length of the output sequence.
tdres is the time resolution (1/sampling rate)
Hinput 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).


zilany2014_ffGn(...) 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. This method is based on an embedding of the covariance matrix in a circulant matrix.

zilany2014_ffgn accepts the following optional parameters:

noiseType : is 0 for fixed fGn noise and 1 for variable fGn. [default = 1] mu : is the mean of the noise. [default = 0] sigma : is the standard deviation of the noise. [default = 1]


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.