# GENERATION OF COLORED NOISE

@article{Bartosch2001GENERATIONOC, title={GENERATION OF COLORED NOISE}, author={Lorenz Bartosch}, journal={International Journal of Modern Physics C}, year={2001}, volume={12}, pages={851-855} }

In this work, we describe a simple Markovian algorithm to generate a typical sample path of colored noise described by an Ornstein–Uhlenbeck process. The algorithm works equally well to simulate a real or complex disorder potential with exponentially decaying covariance and higher correlation functions given by Wick's theorem. As an input, we only need independent Gaussian random numbers which can easily be generated by the well-known Box–Muller algorithm. Finally, we discuss an alternative…

## 38 Citations

### The Entropy Production Distribution in Non-Markovian Thermal Baths

- MathematicsEntropy
- 2014

In this work we study the distribution function for the total entropy production of a Brownian particle embedded in a non-Markovian thermal bath. The problem is studied in the overdamped…

### THE RANDOM SIGNALS SATISFYING THE PROPERTIES OF THE GAUSSIAN WHITE NOISE

- Engineering
- 2005

The random signals de?ned as sums of the single frequency sinusoidal signals with random amplitudes and random phases or equivalently sums of functions obtained by adding a Sine and a Cosine function…

### Stochastic description of the light scattered by a polydisperse colloidal suspension: simulation and experiment.

- MathematicsThe Journal of chemical physics
- 2009

It is proved from Doob's theorem that the electric field scattered by a polydisperse suspension can be accounted for by a linear combination of Ornstein-Uhlenbeck processes.

### Approximate stationary solution and stochastic stability for a class of differential equations with parametric colored noise

- Mathematics
- 2008

This paper aims to study a class of differential equations with parametric Gaussian colored noise. We present the general framework to get the solvability conditions of the approximate stationary…

### Statistics of an autoregressive correlated random walk along a return path

- Mathematics
- 2017

A closed-form analytical solution is derived for the statistical outcome of a random walk along a return path. The random walk is generated from the cumulative sum of correlated samples in a…

### A unified view of hierarchy approach and formula of differentiation.

- MathematicsThe Journal of chemical physics
- 2019

By manipulating the involved Ornstein-Uhlenbeck noise, this work proposes a unified algorithm that may reduce to the hierarchy approach or the formula of differentiation in different limits, and finds that the hierarchy approaches appears to be more efficient for numerical model studies.

### A Spectral Model for RF Oscillators With Power-Law Phase Noise

- PhysicsIEEE Transactions on Circuits and Systems I: Regular Papers
- 2006

It is shown that despite its lack of stationarity it is possible to derive a closed form expression for its effect on an oscillator PSD and that the oscillator output can be considered to be wide-sense stationary.

### Short-window spectral analysis using AMVAR and multitaper methods

- Computer Science2004 International Conference on Signal Processing and Communications, 2004. SPCOM '04.
- 2004

It is demonstrated that the AMVAR method performs better for very short data when compared to the multitaper method, and that coherence can still be detected in noisy bivariate time series data even if the individual power spectra fail to show any peaks.

### Structures in Sound: Analysis of Classical Music Using the Information Length

- PhysicsEntropy
- 2016

The key idea is to envision music as the evolution of a non-equilibrium system and to construct probability distribution functions from musical instrument digital interface (MIDI) files of classical compositions to discuss a way to quantitatively discriminate between music and noise.

### Coherent trapping in small quantum networks

- PhysicsJournal of Statistical Mechanics: Theory and Experiment
- 2019

We consider a three-node fully connected network (Delta network) showing that a coherent population trapping phenomenon occurs, generalizing results for the Lambda network known to support a dark…

## References

SHOWING 1-10 OF 14 REFERENCES

### Fast and precise algorithm for computer simulation of stochastic differential equations.

- Computer SciencePhysical review. A, General physics
- 1989

An algorithm for integrating a set of stochastic differential equations driven by colored noise is presented and the limit of vanishingly small \ensuremath{\tau} can be safely taken, and the algorithm yields the corresponding white-noise quantities in a natural way.

### Fluctuation effects in disordered Peierls systems

- PhysicsAnnalen der Physik
- 2001

We review the density of states (DOS) and related quantities of quasi one‐dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The…

### Stochastic processes in physics and chemistry

- Chemistry, Mathematics
- 1981

Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master…

### An Introduction to Probability Theory and Its Applications

- Mathematics
- 1950

Thank you for reading an introduction to probability theory and its applications vol 2. As you may know, people have look numerous times for their favorite novels like this an introduction to…

### On the Theory of the Brownian Motion

- Mathematics, Materials Science
- 1930

With a method first indicated by Ornstein the mean values of all the powers of the velocity $u$ and the displacement $s$ of a free particle in Brownian motion are calculated. It is shown that…

### Exact numerical calculation of the density of states of the fluctuating gap model

- Physics
- 1999

We develop a powerful numerical algorithm for calculating the density of states rho(omega) of the fluctuating gap model, which describes the low-energy physics of disordered Peierls and spin-Peierls…

### Numerical method for colored-noise generation and its application to a bistable system.

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1990

A methodology for generating sample functions for colored noise which has some relative advantages over existing ones is outlined. This involves simulating a stochastic process in terms of harmonic…

### Comment on "Numerical method for colored-noise generation and its application to a bistable system"

- PhysicsPhysical review. A, Atomic, molecular, and optical physics
- 1992