An approach to handling colored observation noise in large least-squares (LS) problems is presented. The handling of colored noise is reduced to the problem of solving a Toeplitz system of linear equations. The colored noise is represented as an auto regressive moving-average (ARMA) process. Stability and invertability of the ARMA model allows the solution of the Toeplitz system to be reduced t...

We derive the stationary probability distribution for a non-equilibrium system composed by an arbitrary number of degrees of freedom that are subject to Gaussian colored noise and a conservative potential. This is based on a multidimensional version of the Unified Colored Noise Approximation. By comparing theory with numerical simulations we demonstrate that the theoretical probability density ...

In this paper, we define the harmonic oscillator with random damping in non-Markovian thermal bath. This model represents new version of the random oscillators. In this side, we derive the overdamped harmonic oscillator with multiplicative colored noise and translate it into the additive colored noise by changing the variables. The overdamped harmonic oscillator is stochastic differential equat...

This article addresses the impact that colored noise, temporal filtering, and temporal detrending have on the fMRI analysis situation. Specifically, it is shown why the detection of event-related designs benefit more from pre-whitening than blocked designs in a colored noise structure. Both theoretical and empirical results are provided. Furthermore, a novel exploratory method for producing dri...

This paper presents an iterative method for estimating the starting frequency and period slope of hyperbolic frequency modulated (HFM) signals with underwater acoustic platform colored noise. The method involves, firstly, whitening of the colored noise and, secondly, instantaneous frequency (IF) estimation of HFM signals based on the peak of short-time Fourier transform (STFT) and taking recipr...

In this paper, a new combination of Minimum Description Length (MDL) or Eigenvalue Gradient Method (EGM), Joint Approximate Diagonalization of Eigenmatrices (JADE) and Modified Forward-Backward Linear Prediction (MFBLP) algorithms is proposed which determines the number of non-coherent source groups and estimates the Direction Of Arrivals (DOAs) of coherent signals in each group. First, the MDL...

In two recent articles, Rudolph and Destexhe (2003, 2005) studied a leaky integrator model (an RC-circuit) driven by correlated ("colored") gaussian conductance noise and Gaussian current noise. In the first article, they derived an expression for the stationary probability density of the membrane voltage; in the second, they modified this expression to cover a larger parameter regime. Here we ...

In a recent paper, Rudolph and Destexhe (Neural Comp. 15, 2577-2618, 2003) studied a leaky integrator model (i.e. an RC-circuit) driven by correlated (“colored”) Gaussian conductance noise and Gaussian current noise. They derived an expression for the stationary probability density of the membrane voltage. Here we show by standard analysis of solvable limit cases and by numerical simulations th...

The synchronization in four forced FitzHugh–Nagumo (FHN) systems is studied, both experimentally and by numerical simulations of a model. We show that synchronization may be achieved either by coupling of systems through bidirectional diffusive interactions, by introducing a common noise to all systems or by combining both ingredients, noise and coupling together. Here we consider white and col...