# NAME

Math::Random::Brownian - Perl module for generating Fractional Brownian and Gaussian Noise

# SYNOPSIS

`````` use Math::Random::Brownian;
my \$noise = Math::Random::Brownian->new();

my @Hosking_noise = \$noise->Hosking(LENGTH => 30,
HURST => 0.5,
VARIANCE => 1.0,
NOISE => 'Gaussian' );

my @Circ_noise = \$noise->Circulant(LENGTH => 30,
HURST => 0.5,
VARIANCE => 1.0,
NOISE => 'Brownian' );

my @Appr_noise = \$noise->ApprCirc(LENGTH => 30,
HURST => 0.5,
VARIANCE => 1.0,
NOISE => 'Brownian');

my @Paxson = \$noise->Paxson(LENGTH => 30,
HURST => 0.5,
VARIANCE => 1.0,
NOISE => 'Gaussian');``````

# DESCRIPTION

Math::Random::Brownian is a perl module for calculating a realization of either fractional Brownian Motion, or a fractional Gaussian sequence. This is accomplished using the various methods. Currently, the C code for this module is due to Ton Dieker with slight modifications by Walter Szeliga to help the code stand alone. For more information, refer to

Dieker, T. Simulation of fractional Brownian motion, Master's Thesis, University of Twente, Dept. of Mathematical Sciences.

This may be found at http://homepages.cwi.nl/~ton/fbm/.

Hash values and their meanings are as follows:

LENGTH

The length of the realization desired. This must be an integer.

HURST

The Hurst parameter of the output sequence. If A is the slope of a 1/f process, then A = 2H-1 where H is the Hurst parameter.

VARIANCE

The variance of the output sequence.

NOISE

Is equal to either 'Gaussian' or 'Brownian' depending on whether one would like fractional Gaussian noise, or it's cumulative sum -- fractional Brownian motion.

Dieker, T. Simulation of fractional Brownian motion, Master's Thesis, University of Twente, Dept. of Mathematical Sciences.

This may be found at http://homepages.cwi.nl/~ton/fbm/.

For other software, see http://www.geology.cwu.edu/grad/walter

# AUTHOR

Walter Szeliga, <walter@geology.cwu.edu> Original C code by Ton Dieker FFT code by J. Claerbout