scispace - formally typeset
Search or ask a question

Showing papers on "White noise published in 2005"


Journal ArticleDOI
TL;DR: Parsimonious mapping of fMRI noise properties in terms of fGn parameters efficiently estimated in the wavelet domain is feasible and can enhance insight into the pathophysiology of Alzheimer's disease.

284 citations


Journal ArticleDOI
TL;DR: The noise-free transitions between the two basins of attraction that appear in the nonlinear regime are measured, and good agreement with theory is found.
Abstract: We report quantitative measurements of the nonlinear response of a radio frequency mechanical resonator with a very high quality factor. We measure the noise-free transitions between the two basins of attraction that appear in the nonlinear regime, and find good agreement with theory. We measure the transition rate response to controlled levels of white noise, and extract the basin activation energy. This allows us to obtain precise values for the relevant frequencies and the cubic nonlinearity in the Duffing oscillator, with applications to parametric sensing.

217 citations


Journal ArticleDOI
TL;DR: In which way this notation can be extended to Brownian motion of fractional order a (different from 1/2) defined as the Riemann–Liouville derivative of the Gaussian white noise is examined.

186 citations


Journal ArticleDOI
TL;DR: A new measure to determine homogeneous blocks and a new structure analyzer for rejecting blocks with structure based on high-pass operators and special masks for corners to stabilize the homogeneity estimation are proposed.
Abstract: Noise can significantly impact the effectiveness of video processing algorithms. This paper proposes a fast white-noise variance estimation that is reliable even in images with large textured areas. This method finds intensity-homogeneous blocks first and then estimates the noise variance in these blocks, taking image structure into account. This paper proposes a new measure to determine homogeneous blocks and a new structure analyzer for rejecting blocks with structure. This analyzer is based on high-pass operators and special masks for corners to stabilize the homogeneity estimation. For typical video quality (PSNR of 20-40 dB), the proposed method outperforms other methods significantly and the worst-case estimation error is 3 dB, which is suitable for real applications such as video broadcasts. The method performs well both in highly noisy and good-quality images. It also works well in images including few uniform blocks.

182 citations


Journal ArticleDOI
TL;DR: In this paper, the authors investigated whether peak noise or the change in noise level from baseline is more important in inducing sleep disruption and found that white noise added to the environment would reduce arousals by reducing the magnitude of changing noise levels.

180 citations


Journal ArticleDOI
TL;DR: Large white noise can lead to desynchronization of oscillators, provided they are non-isochronous, and this is demonstrated for the Van der Pol-Duffing system.
Abstract: We consider the effect of external noise on the dynamics of limit cycle oscillators. The Lyapunov exponent becomes negative under influence of small white noise, what means synchronization of two or more identical systems subject to common noise. We analytically study the effect of small nonidentities in the oscillators and in the noise, and derive statistical characteristics of deviations from the perfect synchrony. Large white noise can lead to desynchronization of oscillators, provided they are nonisochronous. This is demonstrated for the Van der Pol--Duffing system.

150 citations


Journal ArticleDOI
TL;DR: In this article, the authors consider a model where the logarithm of the squared returns can be decomposed into the sum of a long-memory signal and a white noise, and show that the local Whittle estimator is asymptotically normal for d*∈(0,3/4).
Abstract: We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long-memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long-memory signal and a white noise. We consider periodogram-based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility by allowing the signal process to have a memory parameter d*1/2. We show that the local Whittle estimator is consistent for d*∈(0,1). We also show that the local Whittle estimator is asymptotically normal for d*∈(0,3/4) and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short-memory component of the signal is sufficiently smooth, a convergence rate of n2/5−δ for d*∈(0,3/4) can be attained, where n is the sample size and δ>0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d*=0. This yields a test for long memory in volatility.

135 citations


Journal ArticleDOI
TL;DR: In this paper, a total of 96 absolute gravity (AG) measurements at the Membach station and 221 at the Proudman Oceanographic Laboratory (POL) were analyzed for noise content.
Abstract: [1] A total of 96 absolute gravity (AG) measurements at the Membach station and 221 at the Proudman Oceanographic Laboratory (POL) is analyzed for noise content. The lengths of the series were around 10 years (POL) and 8 years (Membach). First the noise at frequencies lower than 1 cpd is studied. This noise consists in setup-dependent offsets and geophysical colored sources. The setup white noise is estimated using continuous relative superconducting gravity (SG) measurements at Membach. The colored environmental noise affecting both AG and SG is estimated using the maximum likelihood estimation technique to fit two types of stochastic models to the SG time series, power law noise, and first-order Gauss Markov (FOGM) noise. We estimate the noise amplitudes of a white noise process plus power law model while simultaneously solving for the spectral index and the noise amplitudes of a white noise process plus FOGM noise model is also estimated. The gravity rate of change and the associated uncertainties as a function of the noise structure are then computed. At frequencies higher than 1 cpd, a time-varying white noise component usually dominates AG time series. Finally, the POL and Membach experiments are applied to estimate the uncertainties for AG campaigns repeated once or twice a year to monitor crustal deformation. Such repeated AG measurements should allow one to constrain gravity rate of change with an uncertainty of 1 nm s−2 yr−1 (or 0.5 mm yr−1) after 14 or 24 years, depending on the noise model. Therefore long-term measurements using absolute gravimeters are appropriate for monitoring slow vertical tectonic deformation.

132 citations


Journal ArticleDOI
TL;DR: In this article, the first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises, and a detailed analysis of the case of a random damping was performed.
Abstract: The first two moments of an underdamped harmonic oscillator were found for additive and multiplicative noises. A detailed analysis is performed of the case of a random damping which supplements the case of a random frequency which has received the most study. In both cases the second moments are unstable for the sufficient large noise strength. The difference appears in the stability conditions of the first moments which can diverge already for white noise for the random damping and only for color noise for the random frequency. The difference between these two types of multiplicative noises shows up also in the response to an external periodic force, namely white noise influences the first moment only in the case of a random damping. However, the second moments in both cases show the non-monotonic dependence on the noise strength and correlation rate (stochastic resonance in linear systems).

128 citations


Journal ArticleDOI
TL;DR: In this article, an extensible beam equation with a stochastic force of a white noise type is studied, Lyapunov functions techniques are used to prove existence of global mild solutions and asymptotic stability of the zero solution.
Abstract: An extensible beam equation with a stochastic force of a white noise type is studied, Lyapunov functions techniques being used to prove existence of global mild solutions and asymptotic stability of the zero solution.

117 citations


Journal ArticleDOI
TL;DR: Two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed, which provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound for white Gaussian noise before the threshold effect occurs.
Abstract: Based on the linear prediction property of sinusoidal signals, two constrained weighted least squares frequency estimators for multiple real sinusoids embedded in white noise are proposed. In order to achieve accurate frequency estimation, the first algorithm uses a generalized unit-norm constraint, while the second method employs a monic constraint. The weighting matrices in both methods are a function of the frequency parameters and are obtained in an iterative manner. For the case of a single real tone with sufficiently large data samples, both estimators provide nearly identical frequency estimates and their performance approaches Crame/spl acute/r-Rao lower bound (CRLB) for white Gaussian noise before the threshold effect occurs. Algorithms for closed-form single-tone frequency estimation are also devised. Computer simulations are included to corroborate the theoretical development and to contrast the estimator performance with the CRLB for different frequencies, observation lengths and signal-to-noise ratio (SNR) conditions.

Journal ArticleDOI
TL;DR: In this article, a frequency counter measures the input frequency ν¯ averaged over a suitable time τ, versus the reference clock and achieves high resolution by interpolating the clock signal by averaging multiple frequency measurements highly overlapped.
Abstract: A frequency counter measures the input frequency ν¯ averaged over a suitable time τ, versus the reference clock. High resolution is achieved by interpolating the clock signal. Further increased resolution is obtained by averaging multiple frequency measurements highly overlapped. In the presence of additive white noise or white phase noise, the square uncertainty improves from σν2∝1∕τ2 to σν2∝1∕τ3. Surprisingly, when a file of contiguous data is fed into the formula of the two-sample (Allan) variance σy2(τ)=E{12(y¯k+1−y¯k)2} of the fractional frequency fluctuation y, the result is the modified Allan variance mod σy2(τ). But if a sufficient number of contiguous measures are averaged in order to get a longer τ and the data are fed into the same formula, the results is the (nonmodified) Allan variance. Of course interpretation mistakes are around the corner if the counter internal process is not well understood. The typical domain of interest is the the short-term stability measurement of oscillators.

Book
12 Sep 2005
TL;DR: This text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains.
Abstract: Random signals and noise are present in many engineering systems and networks. Signal processing techniques allow engineers to distinguish between useful signals in audio, video or communication equipment, and interference, which disturbs the desired signal. With a strong mathematical grounding, this text provides a clear introduction to the fundamentals of stochastic processes and their practical applications to random signals and noise. With worked examples, problems, and detailed appendices, Introduction to Random Signals and Noise gives the reader the knowledge to design optimum systems for effectively coping with unwanted signals. Key features: • Considers a wide range of signals and noise, including analogue, discrete-time and bandpass signals in both time and frequency domains. • Analyses the basics of digital signal detection using matched filtering, signal space representation and correlation receiver. • Examines optimal filtering methods and their consequences. • Presents a detailed discussion of the topic of Poisson processed and shot noise.

Journal ArticleDOI
TL;DR: It is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense, and the effective-time-constant approximation is identified as the leading-order solution to the full conductance-based model.
Abstract: The subthreshold membrane voltage of a neuron in active cortical tissue is a fluctuating quantity with a distribution that reflects the firing statistics of the presynaptic population. It was recently found that conductancebased synaptic drive can lead to distributions with a significant skew. Here it is demonstrated that the underlying shot noise caused by Poissonian spike arrival also skews the membrane distribution, but in the opposite sense. Using a perturbative method, we analyze the effects of shot noise on the distribution of synaptic conductances and calculate the consequent voltage distribution. To first order in the perturbation theory, the voltage distribution is a gaussian modulated by a prefactor that captures the skew. The gaussian component is identical to distributions derived using current-based models with an effective membrane time constant. The well-known effective-time-constant approximation can therefore be identified as the leading-order solution to the full conductance-based model. The higher-order modulatory prefactor containing the skew comprises terms due to both shot noise and conductance fluctuations. The diffusion approximation misses these shot-noise effects implying that analytical approaches such as the Fokker-Planck equation or simulation with filtered white noise cannot be used to improve on the gaussian approximation. It is further demonstrated that quantities used for fitting theory to experiment, such as the voltage mean and variance, are robust against these non-Gaussian effects. The effective-time-constant approximation is therefore relevant to experiment and provides a simple analytic base on which other pertinent biological details may be added.

Journal ArticleDOI
TL;DR: The source filter model of speech production is adopted as presented in X. Huang et al. (2001), wherein speech is divided into two broad classes: voiced and unvoiced.
Abstract: In this article, we concentrate on spectral estimation techniques that are useful in extracting the features to be used by automatic speech recognition (ASR) system. As an aid to understanding the spectral estimation process for speech signals, we adopt the source filter model of speech production as presented in X. Huang et al. (2001), wherein speech is divided into two broad classes: voiced and unvoiced. Voiced speech is quasi-periodic, consisting of a fundamental frequency corresponding to the pitch of a speaker, as well as its harmonics. Unvoiced speech is stochastic in nature and is best modeled as white noise convolved with an infinite impulse response filter.

Journal ArticleDOI
TL;DR: In this article, it was shown that the design-point excitation is identical to the excitation that generates the mirror image of the free-vibration response when the oscillator is released from a target threshold.

Journal ArticleDOI
TL;DR: A systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken and an MDL-type estimator that is robust against deviation from assumption of equal noise level across the array is studied.
Abstract: Estimating the number of sources impinging on an array of sensors is a well-known and well-investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and nonrobust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years, several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multidimensional searches. In this paper, which is motivated by real-life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL-type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multidimensional searches is presented as well, making this estimator a favorable choice for practical applications.

Journal ArticleDOI
TL;DR: In this article, a random wavelet series representation of fractional process with random exponent (MPRE) was proposed to study their Holder regularity and their self-similarity.
Abstract: Multifractional Processes with Random Exponent (MPRE) are obtained by replacing the Hurst parameter of Fractional Brownian Motion (FBM) with a stochastic process. This process need not be independent of the white noise generating the FBM. MPREs can be conveniently represented as random wavelet series. We will use this type of representation to study their Holder regularity and their self-similarity.

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals and showed that the typical response speed is independent of the high-frequency limit and is set by the rapidness of the AP onset, as revealed by the full transmission function.
Abstract: The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here, we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the θ-neuron, the normal form of the dynamics of Type-I excitable membranes. Using a novel sparse matrix representation of the Fokker-Planck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the high-frequency limit the transmission function decays as ω−γ, where γ surprisingly depends on the phase θ s at which APs are emitted. If at θ s the dynamics is insensitive to external inputs, the transmission function decays as (i) ω−3 for the case of a modulation of a white noise input and as (ii) ω−2 for a modulation of the mean input current in the presence of a correlated and uncorrelated noise as well as (iii) in the case of a modulated amplitude of a correlated noise input. If the insensitivity condition is lifted, the transmission function always decays as ω−1, as in conductance based neuron models. In a physiologically plausible regime up to 1 kHz the typical response speed is, however, independent of the high-frequency limit and is set by the rapidness of the AP onset, as revealed by the full transmission function. In this regime modulations of the noise amplitude can be transmitted faithfully up to much higher frequencies than modulations in the mean input current. We finally show that the linear response approach used is valid for a large regime of stimulus amplitudes.

Journal ArticleDOI
TL;DR: A noise source model, consisting of a pulse sequence at random times with memory, which could be useful to describe physical and biological systems where some delay is present, is presented and it is found that the time behavior of the illness depends on the noise parameters.
Abstract: A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i.e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We find that the time behavior of the illness depends on the noise parameters. Specifically the amplitude and the memory of the noise affect the number of infected people.

Journal ArticleDOI
TL;DR: In this article, the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation was studied.
Abstract: We study the influence of a multiplicative Gaussian noise, white in time and correlated in space, on the blow-up phenomenon in the supercritical nonlinear Schrodinger equation. We prove that any sufficiently regular and localized deterministic initial data gives rise to a solution which blows up in arbitrarily small time with a positive probability.

Proceedings ArticleDOI
21 Aug 2005
TL;DR: This paper shows how to combine several simple techniques -- sketches (random projections), convolution, structured random vectors, grid structures, and combinatorial design -- to achieve high performance windowed Pearson correlation over a variety of data sets.
Abstract: Data arriving in time order (a data stream) arises in fields including physics, finance, medicine, and music, to name a few. Often the data comes from sensors (in physics and medicine for example) whose data rates continue to improve dramatically as sensor technology improves. Further, the number of sensors is increasing, so correlating data between sensors becomes ever more critical in order to distill knowlege from the data. In many applications such as finance, recent correlations are of far more interest than long-term correlation, so correlation over sliding windows (windowed correlation) is the desired operation. Fast response is desirable in many applications (e.g., to aim a telescope at an activity of interest or to perform a stock trade). These three factors -- data size, windowed correlation, and fast response -- motivate this work.Previous work [10, 14] showed how to compute Pearson correlation using Fast Fourier Transforms and Wavelet transforms, but such techniques don't work for time series in which the energy is spread over many frequency components, thus resembling white noise. For such "uncooperative" time series, this paper shows how to combine several simple techniques -- sketches (random projections), convolution, structured random vectors, grid structures, and combinatorial design -- to achieve high performance windowed Pearson correlation over a variety of data sets.

Proceedings ArticleDOI
01 Jan 2005
TL;DR: An algorithm of filtering the noisy real ECG signal and removing the noise interfering R waves at the 4th level detail sequence based on the Donoho et al. algorithm is presented.
Abstract: We present in this paper an algorithm of filtering the noisy real ECG signal. The classical wavelet denoising process, based on the Donoho et al. algorithm, at the 4th level, appears clearly the P and T waves whereas the R waves undergo considerable distortion. This is due to the interference of the WGN and the free noise ECG detail sequences at level 4. To overcome this drawback, our key idea is to estimate the corrupted WGN and consequently remove the noise interfering R waves at the 4th level detail sequence. Our denoising algorithm was applied to a set of the MIT-BIH arrhythmia database ECG records corrupted with a 0 dB WGN which provided an output SNR of around 6 dB and an MSE value of around 0.0011. A comparative analysis using the low pass Butterworth filter and the 4th level classical wavelet denoising provides the output SNR values of around 3 dB and MSE value of around 0.0018; which demonstrates the superior performance of our proposed denoising algorithm

Journal ArticleDOI
TL;DR: In this article, the authors derived the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps and proposed a new procedure for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-Cl estimates.
Abstract: We discuss the derivation of the analytic properties of the cross-power spectrum estimator from multi-detector CMB anisotropy maps. The method is computationally convenient and it provides unbiased estimates under very broad assumptions. We also propose a new procedure for testing for the presence of residual bias due to inappropriate noise subtraction in pseudo-Cl estimates. We derive the analytic behaviour of this procedure under the null hypothesis, and use Monte Carlo simulations to investigate its efficiency properties, which appear very promising. For instance, for full sky maps with isotropic white noise, the test is able to identify an error of 1% on the noise amplitude estimate.

Journal ArticleDOI
TL;DR: In this article, the authors consider the problem of testing a given spatial process for stationarity and isotropy in large heterogeneous fields and propose a spatial spectral analysis based on the homogeneity of a set of spatial spectra evaluated at different locations.

Journal ArticleDOI
TL;DR: Recursive estimation algorithms are obtained without requiring the state-space model generating the signal, but just using covariance information about the signal and the additive noise in the observations as well as the delay probabilities.

Posted Content
TL;DR: In this article, it was shown that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes.
Abstract: We show that the increments of generalized Wiener process, useful to describe non-Gaussian white noise sources, have the properties of infinitely divisible random processes. Using functional approach and the new correlation formula for non-Gaussian white noise we derive directly from Langevin equation, with such a random source, the Kolmogorov's equation for Markovian non-Gaussian process. From this equation we obtain the Fokker-Planck equation for nonlinear system driven by white Gaussian noise, the Kolmogorov-Feller equation for discontinuous Markovian processes, and the fractional Fokker-Planck equation for anomalous diffusion. The stationary probability distributions for some simple cases of anomalous diffusion are derived.

Posted Content
TL;DR: In this article, a simple dynamical model for epidemiological infection with a noise source is presented, where the amplitude and the memory of the noise affect the number of infected people.
Abstract: A noise source model, consisting of a pulse sequence at random times with memory, is presented. By varying the memory we can obtain variable randomness of the stochastic process. The delay time between pulses, i. e. the noise memory, produces different kinds of correlated noise ranging from white noise, without delay, to quasi-periodical process, with delay close to the average period of the pulses. The spectral density is calculated. This type of noise could be useful to describe physical and biological systems where some delay is present. In particular it could be useful in population dynamics. A simple dynamical model for epidemiological infection with this noise source is presented. We find that the time behavior of the illness depends on the noise parameters. Specifically the amplitude and the memory of the noise affect the number of infected people.

Journal ArticleDOI
TL;DR: In this article, the stability of self-sustained oscillations under the influence of external noise was studied and a stationary distribution of the phase was used for an analytic calculation of the maximal Lyapunov exponent.
Abstract: We study the stability of self-sustained oscillations under the influence of external noise. For small-noise amplitude a phase approximation for the Langevin dynamics is valid. A stationary distribution of the phase is used for an analytic calculation of the maximal Lyapunov exponent. We demonstrate that for small noise the exponent is negative, which corresponds to synchronization of oscillators.

Journal ArticleDOI
TL;DR: In this article, completely positive maps that describe noisy, multiparticle unitary operations are depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered.
Abstract: We consider completely positive maps that describe noisy, multiparticle unitary operations. We show that by random single-particle operations the completely positive maps can be depolarized to a standard form with a reduced number of parameters describing the noise process in such a way that the noiseless (unitary) part of the evolution is not altered. A further reduction of the parameters, in many cases even to a single one (i.e., global white noise), is possible by tailoring the decoherence process and increasing the amount of noise. We generalize these results to the dynamical case where the noisy evolution is described by a master equation of Lindblad form, and the noiseless evolution is specified by an interaction Hamiltonian. The resulting standard forms may be used to compute lower bounds on channel capacities, to simplify quantum process tomography or to derive error thresholds for entanglement purification and quantum computation.