THE AUDITORY MODELING TOOLBOX

Applies to version: 1.6.0

View the code

Go to function

zilany2014_ffgn
Generate fast fractional Gaussian noise for zilany2014

Usage:

y = zilany2014_ffGn(N, tdres, Hinput)
y = zilany2014_ffgn(N, tdres, Hinput, noiseType, mu, sigma)

Input parameters:

N Length of the output sequence.
tdres Time resolution (in s, 1/sampling rate).
H

"Hurst" index of the resultant noise. Must be 0 < H \(\leq\) 2). Determines the power spectral density of the output, which will be nominally proportional to \(1/f^{(2H-1)}\):

  • For 0 < H \(\leq\) 1, the output will be fractional Gaussian noise with the Hurst index H.
  • For 1 < H \(\leq\) 2, the output will be fractional Brownian motion with the Hurst index of H-1.
noiseType

Optional type of the noise:

  • 0 for fixed noise.
  • 1 for variable fGn. Default.
mu Optional mean of the noise. Default: 0.
sigma Optional standard deviation of the noise. Default: 1.

Description:

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.

References:

M. S. A. Zilany, I. C. Bruce, and L. H. Carney. Updated parameters and expanded simulation options for a model of the auditory periphery. The Journal of the Acoustical Society of America, 135(1):283--286, Jan. 2014. [ DOI ]

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.

Build with Bootstrap