PINK_NOISE
Samples of a Pink Noise Signal

PINK_NOISE is a C++ library which can generate random values taken from an approximate pink noise signal obeying a 1/f power law.

Licensing:

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

Languages:

PINK_NOISE is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

BLACK_SCHOLES, a C++ library which implements some simple approaches to the Black-Scholes option valuation theory, by Desmond Higham.

COLORED_NOISE, a C++ library which generates samples of noise obeying a 1/f^alpha power law.

CORRELATION, a C++ library which contains examples of statistical correlation functions.

ORNSTEIN_UHLENBECK, a C++ library which approximates solutions of the Ornstein-Uhlenbeck stochastic differential equation (SDE) using the Euler method and the Euler-Maruyama method.

SDE, a C++ library which illustrates the properties of stochastic differential equations (SDE's), and common algorithms for their analysis, by Desmond Higham;

STOCHASTIC_RK, a C++ library which applies a Runge-Kutta scheme to a stochastic differential equation.

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:

• pink_noise.cpp, the source code.
• pink_noise.hpp, the include file.

Examples and Tests:

• pink_noise_test.cpp a sample calling program.
• pink_noise_test.txt, the output file.

List of Routines:

• CDELAY2 is a circular buffer implementation of M-fold delay.
• CORR computes the sample correlation of a signal sample.
• CROSS_CORR computes the sample cross correlation between two signal samples.
• RAN1F is a 1/F random number generator.
• RANH is a hold random number generator of period D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• WRAP2 is a circular wrap of the pointer offset Q.

You can go up one level to the C++ source codes.