cnoise
cnoise,
an Octave code which
generates sequences that simulate 1/f^alpha power law noise. This includes
white noise (alpha = 0), pink noise (alpha = 1) and red or Brownian noise
(alpha = 2), as well as noise for values of alpha between 0 and 2.
cnoise() is based in part on an algorithm by Kasdin,
as cited in the references.
This version of the program is implemented as a function.
The Fourier transform functions that are invoked can handle input
data of any size.
Versions of the algorithm are implemented which generate a vector x
of size N with a 1/f^alpha frequency distribution, with three choices
for the underlying distribution of the white noise vector:
-
f_alpha_uniform ( n, range, alpha ),
a uniform distribution on (-range,+range);
-
f_alpha_gaussian ( n, q_d, alpha ),
a Gaussian distribution with mean 0, variance q_d;
-
f_alpha_tgaussian ( n, q_d, range, alpha ),
a Gaussian distribution with mean 0,
variance q_d, truncated to (-range,range).
Licensing:
The information on this web page is distributed under the MIT license.
Languages:
cnoise is available in
a C version and
a MATLAB version and
an Octave version.
Related Data and Programs:
cnoise_test
colored_noise,
an Octave code which
generates samples of noise obeying a 1/f^alpha power law.
ornstein_uhlenbeck,
an Octave code which
approximates solutions of the ornstein-uhlenbeck
stochastic differential equation (sde) using the euler method and
the euler-maruyama method.
pink_noise,
an Octave code which
computes a pink noise signal obeying a 1/f power law.
stochastic_rk,
an Octave code which
applies a Runge-Kutta scheme to a stochastic differential equation.
Author:
Miroslav Stoyanov,
Oak Ridge National Laboratory.
Reference:
-
Martin Gardner,
White and brown music, fractal curves and one-over-f fluctuations,
Scientific American,
Volume 238, Number 4, April 1978, pages 16-32.
-
Jeremy Kasdin,
Discrete Simulation of Colored Noise and Stochastic Processes
and 1/f^a Power Law Noise Generation,
Proceedings of the IEEE,
Volume 83, Number 5, 1995, pages 802-827.
-
Edoardo Milotti,
1/f noise: a pedagogical review,
arXiv:physics/0204033.
-
Sophocles Orfanidis,
Introduction to Signal Processing,
Prentice-Hall, 1995,
ISBN: 0-13-209172-0,
LC: TK5102.5.O246.
-
William Press,
Flicker Noises in Astronomy and Elsewhere,
Comments on Astrophysics,
Volume 7, Number 4, 1978, pages 103-119.
-
Miroslav Stoyanov, Max Gunzburger, John Burkardt,
Pink Noise, 1/f^alpha Noise, and Their Effect on Solutions
of Differential Equations,
International Journal for Uncertainty Quantification,
Volume 1, Number 3, pages 257-278, 2011.
Source Code:
-
f_alpha_gaussian.m,
generates a discrete colored noise vector of size N with power
spectrum distribution of ALPHA.
White noise is sampled from a Gaussian (0,q_d) distribution.
-
f_alpha_tgaussian.m,
generates a discrete colored noise vector of size N with power
spectrum distribution of ALPHA.
White noise is sampled from a truncated Gaussian distribution
with zero-mean, variance Q_D, and range (-R,+R).
-
f_alpha_uniform.m,
generates a discrete colored noise vector of size N with power
spectrum distribution of ALPHA.
White noise is sampled from a uniform distribution
with range (-R,+R).
-
freq_plotter.m,
performs a numerical test on the frequency distribution of
discrete approximations to a continuous noise field.
Last revised on 20 June 2024.