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White noise

About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.


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TL;DR: In this paper, an extensive set of radial velocities for the star HD 10700 (τ Ceti) was used to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems.
Abstract: Context. The abilities of radial velocity exoplanet surveys to detect the lowest-mass extra-solar planets are currently limited by a combination of instrument precision, lack of data, and 'jitter'. Jitter is a general term for any unknown features in the noise, and reflects a lack of detailed knowledge of stellar physics (asteroseismology, starspots, magnetic cycles, granulation, and other stellar surface phenomena), as well as the possible underestimation of instrument noise. Aims. We study an extensive set of radial velocities for the star HD 10700 (τ Ceti) to determine the properties of the jitter arising from stellar surface inhomogeneities, activity, and telescope-instrument systems, and perform a comprehensive search for planetary signals in the radial velocities. Methods. We performed Bayesian comparisons of statistical models describing the radial velocity data to quantify the number of significant signals and the magnitude and properties of the excess noise in the data. We reached our goal by adding artificial signals to the 'flat' radial velocity data of HD 10700 and by seeing which one of our statistical noise models receives the greatest posterior probabilities while still being able to extract the artificial signals correctly from the data. We utilised various noise components to assess properties of the noise in the data and analyse the HARPS, AAPS, and HIRES data for HD 10700 to quantify these properties and search for previously unknown low-amplitude Keplerian signals. Results. According to our analyses, moving average components with an exponential decay with a timescale from a few hours to few days, and Gaussian white noise explains the jitter the best for all three data sets. Fitting the corresponding noise parameters results in significant improvements of the statistical models and enables the detection of very weak signals with amplitudes below 1 m s-1 level in our numerical experiments. We detect significant periodicities that have no activity-induced counterparts in the combined radial velocities. Three of these signals can be seen in the HARPS data alone, and a further two can be inferred by utilising the AAPS and Keck data. These periodicities could be interpreted as corresponding to planets on dynamically stable close-circular orbits with periods of 13.9, 35.4, 94, 168, and 640 days and minimum masses of 2.0, 3.1, 3.6, 4.3, and 6.6 M⊕, respectively.

149 citations

Journal ArticleDOI
TL;DR: In this article, reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise, are studied.
Abstract: We study reflected solutions of the heat equation on the spatial interval [0, 1] with Dirichlet boundary conditions, driven by an additive space-time white noise. Roughly speaking, at any point (x, t) where the solutionu(x, t) is strictly positive it obeys the equation, and at a point (x, t) whereu(x, t) is zero we add a force in order to prevent it from becoming negative. This can be viewed as an extension both of one-dimensional SDEs reflected at 0, and of deterministic variational inequalities. An existence and uniqueness result is proved, which relies heavily on new results for a deterministic variational inequality.

149 citations

Journal ArticleDOI
Jann-Nan Yang1
TL;DR: In this article, an exploratory study is made to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings, where it is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter.
Abstract: Modern control theory has been successfully applied to control the motions of aerospace vehicles. An exploratory study is made herein to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings. It is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter. The performance index to be minimized consists of the covariances of both the structural responses and the control forces. Under these conditions, the optimal control law is a linear feedback control. The optimal control forces are obtained by solving a matrix Riccati equation. Applications of the optimal control to a multi-degree-of-freedom structure, under stationary wind loads and nonstationary earthquakes, are demonstrated. It is shown that significant reduction in covariances of the structural responses can be achieved by the use of an active control system.

149 citations

Journal ArticleDOI
TL;DR: A model selection criterion for sinusoidal signals in Gaussian noise is derived which also contains the log-likelihood and the penalty terms and reveals remarkable improvement in the selection rule over the commonly used MDL and AIC.
Abstract: The model selection problem for sinusoidal signals has often been addressed by employing the Akaike (1974) information criterion (AIC) and the minimum description length principle (MDL). The popularity of these criteria partly stems from the intrinsically simple means by which they can be implemented. They can, however, produce misleading results if they are not carefully used. The AIC and MDL have a common form in that they comprise two terms, a data term and a penalty term. The data term quantifies the residuals of the model, and the penalty term reflects the desideratum of parsimony. While the data terms of the AIC and MDL are identical, the penalty terms are different. In most of the literature, the AIC and MDL penalties are, however, both obtained by apportioning an equal weight to each additional unknown parameter, be it phase, amplitude, or frequency. By contrast, we demonstrate that the penalties associated with the amplitude and phase parameters should be weighted differently than the penalty attached to the frequencies. Following the Bayesian methodology, we derive a model selection criterion for sinusoidal signals in Gaussian noise which also contains the log-likelihood and the penalty terms. The simulation results disclose remarkable improvement in our selection rule over the commonly used MDL and AIC.

147 citations

Journal ArticleDOI
TL;DR: This numerical study of fractional Brownian noise focuses on determining the limitations of the dispersional analysis method, in particular, assessing the effects of signal length and of added noise on the estimate of the Hurst coefficient,H.
Abstract: Fractal signals can be characterized by their fractal dimension plus some measure of their variance at a given level of resolution. The Hurst exponent, H, is 0.5 for positively correlated series, and = 0.5 for random, white noise series. Several methods are available: dispersional analysis, Hurst rescaled range analysis, autocorrelation measures, and power special analysis. Short data sets are notoriously difficult to characterize; research to define the limitations of the various methods is incomplete. This numerical study of fractional Brownian noise focuses on determining the limitations of the dispersional analysis method, in particular, assessing the effects of signal length and of added noise on the estimate of the Hurst coefficient, H, (which ranges from 0 to 1 and is 2 - D, where D is the fractal dimension). There are three general conclusions: (i) pure fractal signals of length greater than 256 points give estimates of H that are biased but have standard deviations less than 0.1; (ii) the estimates of H tend to be biased toward H = 0.5 at both high H (> 0.8) and low H ( 0.6, and the method is particularly robust for signals with high H and long series, where even 100% noise added has only a few percent effect on the estimate of H. Dispersional analysis can be regarded as a strong method for characterizing biological or natural time series, which generally show long-range positive correlation.

147 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023238
2022535
2021488
2020541
2019558
2018537