colored_noise

colored_noise, 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 brown noise or Brownian motion (alpha = 2), but also values of alpha between 0 and 2.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

colored_noise is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

colored_noise_test

brownian_motion_simulation, an Octave code which simulates Brownian motion in an M-dimensional region.

cnoise, an Octave code which generates samples of noise obeying a 1/f^alpha power law, by Miroslav Stoyanov.

correlation, an Octave code which contains examples of statistical correlation functions.

normal, an Octave code which computes elements of a sequence of pseudorandom normally distributed values.

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.

sftpack, an Octave code which implements the "slow" Fourier transform, intended as a teaching tool and comparison with the fast Fourier transform.

stochastic_rk, an Octave code which applies a Runge-Kutta scheme to a stochastic differential equation.

uniform, an Octave code which computes elements of a uniform pseudorandom sequence.

Reference:

1. Martin Gardner,
   White and brown music, fractal curves and one-over-f fluctuations,
   Scientific American,
   Volume 238, Number 4, April 1978, pages 16-32.
2. 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.
3. Edoardo Milotti,
   1/f noise: a pedagogical review,
   arXiv:physics/0204033.
4. Sophocles Orfanidis,
   Introduction to Signal Processing,
   Prentice-Hall, 1995,
   ISBN: 0-13-209172-0,
   LC: TK5102.5.O246.
5. William Press,
   Flicker Noises in Astronomy and Elsewhere,
   Comments on Astrophysics,
   Volume 7, Number 4, 1978, pages 103-119.
6. 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.m generates a 1/F^ALPHA noise sequence.
• make_plots.m an Octave code which reads the "txt" files and makes plots.
• r8_normal_01.m returns a unit pseudonormal R8.
• r8_uniform_01.m returns a unit pseudorandom R8.
• r8vec_print.m prints an R8VEC.
• r8vec_print_part.m prints "part" of an R8VEC.
• r8vec_sftb.m computes a "slow" backward Fourier transform of real data.
• r8vec_sftf.m computes a "slow" forward Fourier transform of real data.