Colored Noise Research Papers - Academia.edu (original) (raw)

The Novikov–Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by... more

The Novikov–Furutsu (NF) theorem is a well-known mathematical tool, used in stochastic dynamics for correlation splitting, that is, for evaluating the mean value of the product of a random functional with a Gaussian argument multiplied by the argument itself. In this work, the
NF theorem is extended for mappings (function-functionals) of two arguments, one being a random variable and the other a random function, both of which are Gaussian, may have nonzero mean values, and may be correlated with each other. This extension allows for the study of random differential equations under coloured noise excitation, which may be correlated with the random initial value. Applications in this direction are briefly discussed. The proof of the extended NF theorem is based on a more general result, also proven herein by using Volterra functional calculus, stating that: the mean value of a general, nonlinear function-functional having random arguments, possibly non-Gaussian, can be expressed in terms of the characteristic functional of its arguments. Generalizations to the multidimensional case (multivariate random arguments) are also presented.

Stabilisability of an open loop unstable plant is studied under the presence of a bandwidth limited additive coloured noise communication channel with constrained signal to noise ratio. The problem is addressed through the use of an LTI... more

Stabilisability of an open loop unstable plant is studied under the presence of a bandwidth limited additive coloured noise communication channel with constrained signal to noise ratio. The problem is addressed through the use of an LTI filter explicitly modelling the bandwidth limitation, and another LTI filter to model the additive coloured noise. Results in this paper show that a bandwidth limitation increases the minimum value of signal to noise ratio required for stabilisability, in comparison to the infinite bandwidth, white noise case. Examples are used to illustrate the results in the continuous and discrete framework

This work studies the spatio-temporal dynamics,of a generic integral‐differential equation subject to additive random,fluctuations. It introduces a combination,of the stochastic center manifold,approach for stochastic differential... more

This work studies the spatio-temporal dynamics,of a generic integral‐differential equation subject to additive random,fluctuations. It introduces a combination,of the stochastic center manifold,approach for stochastic differential equations and the adiabatic elimination for Fokker‐Planck equations, and studies analytically the systems’ stability near Turing bifurcations. In addition two types of fluctuation are studied, namely fluctuations uncorrelated in space and time, and global

We consider the stochastic heat equation with multiplicative noise ut=frac12Deltau+udotWu_{t}=\frac{1}{2}\Delta u+u\dot{W}ut=frac12Deltau+udotW in ℝ+×ℝd , whose solution is interpreted in the mild sense. The noise dotW\dot{W}dotW is fractional in time (with Hurst index H≥1/2), and... more

We consider the stochastic heat equation with multiplicative noise ut=frac12Deltau+udotWu_{t}=\frac{1}{2}\Delta u+u\dot{W}ut=frac12Deltau+udotW in ℝ+×ℝd , whose solution is interpreted in the mild sense. The noise dotW\dot{W}dotW is fractional in time (with Hurst index H≥1/2), and colored in space (with spatial covariance kernel f). When H>1/2, the equation generalizes the Itô-sense equation for H=1/2. We prove that if f is the Riesz kernel of order α, or the Bessel kernel of order α<d, then the sufficient condition for the existence of the solution is d≤2+α (if H>1/2), respectively d<2+α (if H=1/2), whereas if f is the heat kernel or the Poisson kernel, then the equation has a solution for any d. We give a representation of the kth order moment of the solution in terms of an exponential moment of the “convoluted weighted” intersection local time of k independent d-dimensional Brownian motions.

We use the influence functional path-integral method to derive an exact master equation for the quantum Brownian motion of a particle linearly coupled to a general environment (ohmic, subohmic, or supraohmic) at arbitrary temperature and... more

We use the influence functional path-integral method to derive an exact master equation for the quantum Brownian motion of a particle linearly coupled to a general environment (ohmic, subohmic, or supraohmic) at arbitrary temperature and apply it to study certain aspects of ...

Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic... more

Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present work, such equations are derived for a scalar, nonlinear RDE under additive coloured Gaussian noise excitation, through the stochastic Liouville equation. The latter is an exact, yet non-closed equation, involving averages over the time history of the non-Markovian response. This non-locality is treated by applying an extension of the Novikov-Furutsu theorem and a novel approximation, employing a stochastic Volterra-Taylor functional expansion around instantaneous response moments, leading to efficient, closed, approximate equations for the response pdf. These equations retain a tractable amount of non-locality and nonlinearity, and they are valid in both the transient and long-time regimes for any correlation function of the excitation. Also, they include as special cases various existing relevant models, and generalize Hänggi's ansatz in a rational way. Numerical results for a bistable nonlinear RDE confirm the accuracy and the efficiency of the new equations. Extension to the multidimensional case (systems of RDEs) is feasible, yet laborious.

We propose a watermarking scheme to hide copyright information in an image. The scheme employs visual masking to guarantee that the embedded watermark is invisible and to maximize the robustness of the hidden data. The watermark is... more

We propose a watermarking scheme to hide copyright information in an image. The scheme employs visual masking to guarantee that the embedded watermark is invisible and to maximize the robustness of the hidden data. The watermark is constructed for arbitrary image blocks by filtering a pseudo-noise sequence (author id) with a filter that approximates the frequency masking characteristics of the visual system. The noise-like watermark is statistically invisible to deter unauthorized removal. Experimental results show that the watermark is robust to several distortions including white and colored noises, JPEG coding at different qualities, and cropping

We describe a "constant pace" framework for video summarization via fast playback or temporal sub-sampling. The pace of the summary serves as a parameter that enables production of a video summary of any desired length. Earlier, we showed... more

We describe a "constant pace" framework for video summarization via fast playback or temporal sub-sampling. The pace of the summary serves as a parameter that enables production of a video summary of any desired length. Earlier, we showed that the intensity of motion activity (or pace) of a video sequence is a good indication of its "summarizability". Here we build on this notion by adapting the playback frame-rate or the temporal subsampling rate to the pace. Either the less active parts of the sequence are played back at a faster frame rate or the less active parts of the sequence are sub-sampled more heavily than are the more active parts, so as to produce a summary with constant pace. The basic idea is to skip over the less interesting parts of the video. Our technique is computationally simple and gives satisfactory results with surveillance and entertainment video

Single channel enhancement techniques based on short-time spectral amplitude (STSA) estimation have the major drawback of generating an artificial and annoying residual noise with musical character, due mainly to the unwanted peaks in the... more

Single channel enhancement techniques based on short-time spectral amplitude (STSA) estimation have the major drawback of generating an artificial and annoying residual noise with musical character, due mainly to the unwanted peaks in the denoised signal spectrum. The detection and reduction of spectral peaks which have a musical characteristic are the main objectives of this paper. The proposed perceptual technique to reduce musical residual noise operates as a post-processing. Based on human auditory properties, the perceptual post-processing is established in a number of steps. First, we detect musical peaks by comparing tonality coefficients in each critical band of both denoised signal and reference signal. Detected musical peaks are audible only if they exceed the clean speech masking threshold (MT). However, the clean MT is not available. It is estimated by modifying the Johnston model. Secondly, we reduce the musical residual noise by removing only audible musical peaks which exceed the estimated MT. The proposed method is tested and compared with classic STSA technique and perceptual techniques at various levels of white and colored noise. Results show the validity of the proposed technique.

Abstract: There are many situations where speech is affected by different kind of acoustic noise. We propose an improved spectral subtraction method for the reduction of colored acoustic noise added to the speech. Our implementation uses... more

Abstract: There are many situations where speech is affected by different kind of acoustic noise. We propose an improved spectral subtraction method for the reduction of colored acoustic noise added to the speech. Our implementation uses a multi-band spectral over ...