Case Of White Noise Research Articles

Effect of realistic and filtered stellar photometric noise on the detection of moons using photometric transit timing

The photometric transit timing technique was proposed by Szabo et al. (2006) as a method for discovering moons of transiting extrasolar planets. In the preliminary analysis of this technique, it was assumed that the noise in the transit lightcurve was well described by uncorrelated white noise. However, this assumption is not necessarily realistic. To determine the effect of using more realistic lightcurves, transit timing uncertainties are calculated for the case of white noise, measured solar photometric noise and measured solar photometric noise that has been filtered. It is found that for light curves contaminated with realistic photometric noise, the transit timing uncertainties are dramatically increased (and thus moon detection reduced). In addition, we find that while filtering reduced this problem, it did not negate it.

A Simple Precoding-Based Blind Channel Estimation for Space-Time Block-Coded Single-Carrier With Frequency-Domain Equalization Systems

We propose a blind channel estimation method for space-time block-coded single-carrier with frequency-domain equalization (SC-FDE) systems based on a simple, nonredundant precoding. This method of precoding allows us to better structure the relation between the covariance matrices of the received data and the products of channel coefficients. Using this structure, we can easily obtain the products of channel coefficients by using only subtraction and division. Then each of the two channel impulse response vectors is obtained by computing the eigenvector that is associated with the maximal eigenvalue of a Hermitian matrix formed from the corresponding products of channel coefficients. The proposed framework guarantees the unique recovery of all the products of channel coefficients for colored or white noise cases. The impact of the precoding on channel estimation and equalization is also discussed. Simulations are used to demonstrate the performance of the proposed method.

Brownian motors: Joint effect of non-Gaussian noise and time asymmetric forcing

Previous works have shown that time asymmetric forcing on the one hand, as well as non-Gaussian noises on the other, can separately enhance the efficiency and current of a Brownian motor. Here, we study the result of subjecting a Brownian motor to both effects simultaneously. Our results have been compared with those obtained for the Gaussian white noise regime in the adiabatic limit. We find that, although the inclusion of the time asymmetry parameter increases the efficiency value up to a certain extent, for the present case this increase is much less appreciable than in the white noise case. We also present a comparative study of the transport coherence in the context of colored noise. Though the efficiency in some cases becomes higher for the non-Gaussian case, the Péclet number is always higher in the Gaussian colored noise case than in the white noise as well as non-Gaussian colored noise cases.

The stochastic wave equation with fractional noise: A random field approach

We consider the linear stochastic wave equation with spatially homogeneous Gaussian noise, which is fractional in time with index H > 1 / 2 . We show that the necessary and sufficient condition for the existence of the solution is a relaxation of the condition obtained in Dalang (1999) [10], where the noise is white in time. Under this condition, we show that the solution is L 2 ( Ω ) -continuous. Similar results are obtained for the heat equation. Unlike in the white noise case, the necessary and sufficient condition for the existence of the solution in the case of the heat equation is different (and more general) than the one obtained for the wave equation.

Synchronization transition in the Kuramoto model with colored noise

We present a linear stability analysis of the incoherent state in a system of globally coupled identical phase oscillators subject to colored noise. In that we succeed to bridge the extreme time scales between the formerly studied and analytically solvable cases of white noise and quenched random frequencies.

A new critical theorem for adaptive nonlinear stabilization

It is fairly well known that there are fundamental differences between adaptive control of continuous-time and discrete-time nonlinear systems. In fact, even for the seemingly simple single-input single-output control system y t + 1 = θ 1 f ( y t ) + u t + w t + 1 with a scalar unknown parameter θ 1 and noise disturbance { w t } , and with a known function f ( ⋅ ) having possible nonlinear growth rate characterized by | f ( x ) | = Θ ( | x | b ) with b ≥ 1 , the necessary and sufficient condition for the system to be globally stabilizable by adaptive feedback is b < 4 . This was first found and proved by Guo (1997) for the Gaussian white noise case, and then proved by Li and Xie (2006) for the bounded noise case. Subsequently, a number of other types of “critical values” and “impossibility theorems” on the maximum capability of adaptive feedback were also found, mainly for systems with known control parameter as in the above model. In this paper, we will study the above basic model again but with additional unknown control parameter θ 2 , i.e., u t is replaced by θ 2 u t in the above model. Interestingly, it turns out that the system is globally stabilizable if and only if b < 3 . This is a new critical theorem for adaptive nonlinear stabilization, which has meaningful implications for the control of more general uncertain nonlinear systems.

Brownian motion in a solitary potential well in a bounded solid structure

The motion of a heavy Brownian particle in a low-dimensional bounded solid structure under the effect of a phonon’s excitation fluctuations is considered. Because of the finiteness of the system, the fluctuation spectrum has zero spectral density at zero frequency. The effect of this kind of noise, which is conditionally called “green” noise, is studied both analytically by using the averaging method and numerically on the basis of predictor-corrector algorithms. The effective potential is introduced, and its form is shown to govern the particle dynamics. Considering a Gaussian potential well (a trap) as an example, it is demonstrated that green noise leads to abrupt phase transitions in the system as a result of very small parameter variations (a catastrophe-type effect). The results are compared with the case of white noise in an unbounded structure. From numerical calculations, it follows that the boundedness of the structure, which changes the noise spectrum, favors a considerable increase in the lifetime of the particle in the trap.

Contour representation of sound signals

Event Abstract Back to Event Contour representation of sound signals Yoonseob Lim1*, Barbara G. Shinn-Cunningham1 and Timothy Gardner2 1 Boston University, Department of Cognitive and Neural Systems, United States 2 Boston University, Faculty of Electrical Engineering and Computing, United States Continuous edges, or contours, are powerful features for object recognition, both in neural and machine vision. Similarly, auditory signals are characterized by sharp edges in some classes of time-frequency analysis. Linking these edges to form contours could be relevant for auditory signal processing. However, the mathematical foundations of a general contour representation of sound have not been established. Sinusoidal representations of voiced speech and music have been explored, but these approaches do not represent broadband signals efficiently. Here we construct a two-dimensional contour representation that is generally applicable to any time series, including sound. Starting with the Short Time Fourier Transform (STFT), the method defines edges by coherent phase structure at local points in the time-frequency plane (zero crossings of a complex reassignment matrix). Continuous edges are grouped to form contours that follow the ridges and valleys of the traditional STFT. Local amplitudes are assigned by calculation of fixed points in an iterated reassignment mapping. The representation is additive; the complex amplitudes of the contours can be directly summed to reproduce the original signal. This re-synthesis matches the original signal with a signal-to-noise ratio of 15 dB or higher, even in the challenging case of white noise. In practice, this level of precision provides perceptually equivalent representations of speech and music. For many sounds of interest, a subset of the full contour collection can provide an accurate representation. To find this compact subset, an over-complete set of contours are calculated using multiple filter bandwidths. Contours are then ranked by power, length and curvature, and subject to lateral inhibition from neighboring contours. The top-ranking contours in this distribution provide a sparse representation that emerges without any prior suppositions about the nature of the original signal. By combining contours from multiple bandwidths, the representation achieves high precision in both time and frequency. As such, the method is relevant to a wide range of time-frequency tasks such as constructing receptive fields of auditory neurons, characterizing animal vocalizations, pattern recognition and signal de-noising. We speculate that neural auditory processing involves a similar contour representation. Each stage in the analysis is a plausible operation for neurons: parallel and redundant primary processing in multiple bandwidths, grouping by phase coherence, linking by continuity and lateral inhibition. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session I Citation: Lim Y, Shinn-Cunningham BG and Gardner T (2010). Contour representation of sound signals. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00133 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 01 Mar 2010; Published Online: 01 Mar 2010. * Correspondence: Yoonseob Lim, Boston University, Department of Cognitive and Neural Systems, Boston, United States, yslim@bu.edu Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Yoonseob Lim Barbara G Shinn-Cunningham Timothy Gardner Google Yoonseob Lim Barbara G Shinn-Cunningham Timothy Gardner Google Scholar Yoonseob Lim Barbara G Shinn-Cunningham Timothy Gardner PubMed Yoonseob Lim Barbara G Shinn-Cunningham Timothy Gardner Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

The influence of seasonal signals on the estimation of the tectonic motion in short continuous GPS time-series

Abstract Most GPS time-series exhibit a seasonal signal that can have an amplitude of a few millimetres. This seasonal signal can be removed by fitting an extra sinusoidal signal with a period of one year to the GPS data during the estimation of the linear trend. However, Blewitt and Lavallee (2002) showed that including an annual signal in the estimation process still can give a larger linear trend error than the trend error estimated from data from which the annual signal has been removed by other means. They assumed that the GPS data only contained white noise and we extend their result to the case of power-law plus white noise which is known to exist in most GPS observations. For the GPS stations CASC, LAGO, PDEL and TETN the difference in trend error between having or not having an annual signal in the data is around ten times larger when a power-law plus white noise model is used instead of a pure white noise model. Next, our methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time-series by using a physical model. Finally, we demonstrate that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data. This causes on average an underestimation of the trend error.

Pathwise uniqueness for stochastic heat equations with Hölder continuous coefficients: the white noise case

We prove pathwise uniqueness for solutions of parabolic stochastic pde’s with multiplicative white noise if the coefficient is Holder continuous of index γ > 3/4. The method of proof is an infinite-dimensional version of the Yamada–Watanabe argument for ordinary stochastic differential equations.

Malliavin calculus and decoupling inequalities in Banach spaces

We develop a theory of Malliavin calculus for Banach space-valued random variables. Using radonifying operators instead of symmetric tensor products we extend the Wiener–Itô isometry to Banach spaces. In the white noise case we obtain two sided L p -estimates for multiple stochastic integrals in arbitrary Banach spaces. It is shown that the Malliavin derivative is bounded on vector-valued Wiener–Itô chaoses. Our main tools are decoupling inequalities for vector-valued random variables. In the opposite direction we use Meyer's inequalities to give a new proof of a decoupling result for Gaussian chaoses in UMD Banach spaces.

Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties

We analyze the non-Markovian dynamics of a quantum system subject to spontaneous collapse in space. After having proved, under suitable conditions, the separation of the center-of-mass and relative motions, we focus our analysis on the time evolution of the center of mass of an isolated system (free-particle case). We compute the explicit expression of the Green's function, for a generic Gaussian noise, and analyze in detail the case of an exponential correlation function. We study the time evolution of average quantities, such as the mean position, momentum, and energy. We eventually specialize to the case of Gaussian wave functions and prove that all basic facts about collapse models, which are known to be true in the white-noise case, hold also in the more general case of non-Markovian dynamics.

Testing for linear vector autoregressive dynamics under multivariate generalized autoregressive heteroskedasticity

In this paper, we propose a fixed design wild bootstrap procedure to test parameter restrictions in vector autoregressive models, which is robust in cases of conditionally heteroskedastic error terms. The wild bootstrap does not require any parametric specification of the volatility process and takes contemporaneous error correlation implicitly into account. Via a Monte Carlo investigation, empirical size and power properties of the method are illustrated for the case of white noise under the null hypothesis. We compare the bootstrap approach with standard ordinary least squares (OLS)‐based, weighted least squares (WLS) and quasi‐maximum likelihood (QML) approaches. In terms of empirical size, the proposed method outperforms competing approaches and achieves size‐adjusted power close to WLS or QML inference. A White correction of standard OLS inference is satisfactory only in large samples. We investigate the case of Granger causality in a bivariate system of inflation expectations in France and the United Kingdom. Our evidence suggests that the former are Granger causal for the latter while for the reverse relation Granger non‐causality cannot be rejected.

Noise effects in two different biological systems

We investigate the role of the colored noise in two biological systems: (i) adults of Nezara viridula (L.) (Heteroptera: Pentatomidae), and (ii) polymer translocation. In the first system we analyze, by directionality tests, the response of N. viridula individuals to subthreshold signals plus noise in their mating behaviour. The percentage of insects that react to the subthreshold signal shows a nonmonotonic behaviour, characterized by the presence of a maximum, as a function of the noise intensity. This is the signature of the non-dynamical stochastic resonance phenomenon. By using a “soft” threshold model we find that the maximum of the input-output cross correlation occurs in the same range of noise intensity values for which the behavioural activation of the insects has a maximum. Moreover this maximum value is lowered and shifted towards higher noise intensities, compared to the case of white noise. In the second biological system the noise driven translocation of short polymers in crowded solutions is analyzed. An improved version of the Rouse model for a flexible polymer is adopted to mimic the molecular dynamics by taking into account both the interactions between adjacent monomers and the effects of a Lennard-Jones potential between all beads. The polymer dynamics is simulated in a two-dimensional domain by numerically solving the Langevin equations of motion in the presence of thermal fluctuations and a colored noise source. At low temperatures or for strong colored noise intensities the translocation process of the polymer chain is delayed. At low noise intensity, as the polymer length increases, we find a nonmonotonic behaviour for the mean first translocation time of the polymer centre of inertia. We show how colored noise influences the motion of short polymers, by inducing two different regimes of translocation in the dynamics of molecule transport.

Role of Spectral Peaks in Autocoorelation Domain for Robust Speech Recognition

This paper presents a new front-end for robust speech recognition. This new front-end scenario focuses on the spectral features of the filtered speech signals in the autocorrelation domain. The autocorrelation domain is well known for its pole preserving and noise separation properties. In this paper we will use the autocorrelation domain as an appropriate candidate for robust feature extraction. The proposed method introduces a novel representation of speech for the cases where the speech signal is corrupted by additive noises. In this method, the speech features are computed by reducing additive noise effects via an initial filtering stage, followed by the extraction of autocorrelation spectrum peaks. Robust features based on theses peaks are derived by assuming that the corrupting noise is stationary in nature. A task of speaker-independent isolated-word recognition is used to demonstrate the efficiency of these robust features. The cases of white noise and colored noise such as factory, babble and F16 are tested. Experimental results show significant improvement in comparison to the results obtained using traditional front end methods. Further enhancement has been done by applying cepstral mean normalization (CMN) on the above extracted features.

Novel Stochastic Modeling and Filtering of the Attitude Quaternion

A novel continuous-time stochastic differential equation (SDE) for spacecraft attitude quaternion kinematics with state-multiplicative noise and a novel continuous-time exact optimal quaternion filter are developed in the framework of Ito (mean-square) calculus. The quaternion Ito SDE contains dissipative terms that ensure the mean-square stability of the process. Closed-form deterministic propagation equations are developed for the second-order moment of the quaternion. The quaternion filter produces the linear minimum-variance unbiased estimate of the quaternion from continuous observations with additive white noise. The filter gain computations include coupled Riccati equations of the estimation error matrix and of the quaternion second-order moment. These computations are not estimate-dependent and can therefore be performed off-line. The special case of gyro error white noise with independent identically distributed components is considered. The case of correlated components can be addressed straightforwardly. Additive gyro biases are easily handled via state augmentation. Extensive Monte-Carlo simulations are performed in order to validate the Ito model and to illustrate the proposed filter accuracy. Comparative simulations of the novel filter and of a standard additive extended Kaiman filter are performed both for attitude-only estimation and for attitude-bias estimation. For practical purposes, the novel modeling and filtering approach shows similar results as the standard approach when the process noise level is low. For high signal-to-noise ratio however, the numerical study suggests that the novel filter can increase the accuracy of a conventional Kaiman by orders of magnitudes.

Discrete Wirtinger-Type Inequalities for Gauging the Power of Sinusoids Buried in Noise

Two discrete-time Wirtinger-type inequalities relating the power of a finite-length signal to that of its circularly-convolved version are developed. The usual boundary conditions that accompany the existing Wirtinger-type inequalities are relaxed in the proposed inequalities and the equalizing sinusoidal signal is free to have an arbitrary phase angle. A measure of this sinusoidal signal's power, when corrupted with additive noise, is proposed. The application of the proposed measure, calculated as a ratio, in the evaluation of the power of a sinusoid of arbitrary phase with the angular frequency π/N, where N is the signal length, is thoroughly studied and analyzed under additive noise of arbitrary statistical characteristic. The ratio can be used to gauge the power of sinusoids of frequency π/N with a small amount of computation by referring to a ratio-versus-SNR curve and using it to make an estimation of the noise-corrupted sinusoid's SNR. The case of additive white noise is also analyzed. A sample permutation scheme followed by sign modulation is proposed for enlarging the class of target sinusoids to those with frequencies Mπ/N, where M and N are mutually prime positive integers. Tandem application of the proposed scheme and ratio offers a simple method to gauge the power of sinusoids buried in noise. The generalization of the inequalities to convolution kernels of higher orders as well as the simplification of the proposed inequalities have also been studied.

Performance analysis of decision-feedback equalisation for cellular mobile radio with cochannel interference and fading

The error probability of minimum-mean-square-error decision-feedback equalisation (MMSE-DFE) is evaluated for digital cellular mobile radio systems in the presence of cochannel interference (CCI) and is compared with linear equalisation (LE). The main contribution of the paper is that this analysis accounts for pulse waveform, modulation and fading of the signal of interest, as well as the CCI. Quadrature-amplitude modulation (QAM) signalling in frequency-selective and quasi-static channels is considered. The CCI is treated as a stationary process, when caused by random phase and symbol-timing offsets relative to the signal of interest. Analysis includes techniques combining antenna diversity. The performance improvement as a function of taps in both feedforward and feedback filters is quantified. Owing to residual intersymbol interference (ISI) and CCI, the evaluation of the error probability is extremely complicated and time consuming in simulation. To overcome this issue, an efficient method based upon Gauss quadrature rules (GQR) is presented to compute the error probability. The method is not limited due to interference statistics and it yields remarkable advantages compared with other methods. The convergence of finite-length results to their infinite-length counterparts is also provided. Unlike the case of white noise, the simulations reveal that with the same finite length the DFE is unable to outperform the linear equaliser in a CCI-dominated channel if the feedback filter is of insufficient length.

Exponential growth and Gaussian—like fluctuations of solutions of stochastic differential equations with maximum functionals

In this paper we consider functional differential equations subjected to either instantaneous state-dependent noise, or to a white noise perturbation. The drift of the equations depend linearly on the current value and on the maximum of the solution. The functional term always provides positive feedback, while the instantaneous term can be mean-reverting or can exhibit positive feedback. We show in the white noise case that if the instantaneous term is mean reverting and dominates the history term, then solutions are recurrent, and upper bounds on the a.s. growth rate of the partial maxima of the solution can be found. When the instantaneous term is weaker, or is of positive feedback type, we determine necessary and sufficient conditions on the diffusion coefficient which ensure the exact exponential growth of solutions. An application of these results to an inefficient financial market populated by reference traders and speculators is given, in which the difference between the current instantaneous returns and maximum of the returns over the last few time units is used to determine trading strategies.

Verhulst model with Lévy white noise excitation

The transient dynamics of the Verhulst model perturbed by arbitrary non-Gaussian white noise is investigated. Based on the infinitely divisible distribution of the Levy process we study the nonlinear relaxation of the population density for three cases of white non-Gaussian noise: (i) shot noise, (ii) noise with a probability density of increments expressed in terms of Gamma function, and (iii) Cauchy stable noise. We obtain exact results for the probability distribution of the population density in all cases, and for Cauchy stable noise the exact expression of the nonlinear relaxation time is derived. Moreover starting from an initial delta function distribution, we find a transition induced by the multiplicative Levy noise, from a trimodal probability distribution to a bimodal probability distribution in asymptotics. Finally we find a nonmonotonic behavior of the nonlinear relaxation time as a function of the Cauchy stable noise intensity.