# THE AUDITORY MODELING TOOLBOX

Applies to version: 1.1.0

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

## Usage

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) 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). 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.

## Description

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.

## References:

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.