White noise

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

Wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra

Abstract: We derive minimax rates for estimation in anisotropic smoothness classes. This rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension. It is shown that this basis is superior to its one-scale multiresolution analog, if different degrees of smoothness in different directions are present.; As an important application we introduce a new adaptive wavelet estimator of the time-dependent spectrum of a locally stationary time series. Using this model which was resently developed by Dahlhaus, we show that the resulting estimator attains nearly the rate, which is optimal in Gaussian white noise, simultaneously over a wide range of smoothness classes. Moreover, by our new approach we overcome the difficulty of how to choose the right amount of smoothing, i.e. how to adapt to the appropriate resolution, for reconstructing the local structure of the evolutionary spectrum in the time-frequency plane.

Flows, coalescence and noise

Abstract: We are interested in stationary “fluid” random evolutions with independent increments. Under some mild assumptions, we show they are solutions of a stochastic differential equation (SDE). There are situations where these evolutions are not described by flows of diffeomorphisms, but by coalescing flows or by flows of probability kernels. In an intermediate phase, for which there exist a coalescing flow and a flow of kernels solution of the SDE, a classification is given: All solutions of the SDE can be obtained by filtering a coalescing motion with respect to a subnoise containing the Gaussian part of its noise. Thus, the coalescing motion cannot be described by a white noise.

Robust H/sub /spl infin// filtering of stationary continuous-time linear systems with stochastic uncertainties

Abstract: The problem of applying H/sub /spl infin// filters on stationary, continuous-time, linear systems with stochastic uncertainties in the state-space signal model is addressed. These uncertainties are modeled via white noise processes. The relevant cost function is the expected value of the standard H/sub /spl infin// performance index with respect to the uncertain parameters. The solution is obtained via a stochastic bounded real lemma that results in a modified Riccati inequality. This inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters. The method proposed is also applied to the case where, in addition to the stochastic uncertainty, other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope. The problem of mixed H/sub 2//H/sub /spl infin// filtering for the above system is also treated. The theory developed is demonstrated by a practical example.

A time-frequency formulation of optimum detection

Abstract: A time-frequency formulation is proposed for the optimum detection of Gaussian signals in white Gaussian noise. By choosing the Wigner-Ville distribution as the basic time-frequency tool, it is shown that the corresponding receivers generally take the form of a correlation between time-frequency structures, matching mathematical optimality with a physically meaningful interpretation. The case of low SNR is examined and various examples are considered: deterministic signal, Rayleigh fading signal, random jitter, and random time-varying channel. A general class of time-frequency receivers is proposed which admits as limiting cases different known structures, and its suboptimum performance is evaluated. Possible extensions to more elaborate situations (including parameter estimation) are mentioned. >

Feature Extraction for Short-Circuit Fault Detection in Permanent-Magnet Synchronous Motors Using Stator-Current Monitoring

Abstract: In this paper, a novel frequency pattern and competent criterion are introduced for short-circuit-fault recognition in permanent-magnet synchronous motors (PMSMs). The frequency pattern is extracted from the monitored stator current analytically and the amplitude of sideband components at these frequencies is introduced as a proper criterion to determine the number of short-circuited turns. Impacts of the load variation on the proposed criterion are investigated in the faulty PMSM. In order to demonstrate the aptitude of the proposed criterion for precise short-circuit fault detection, the relation between the nominated criterion and the number of short-circuited turns is specified by the mutual information index. Therefore, a white Gaussian noise is added to the simulated stator current and robustness of the criterion is analyzed with respect to the noise variance. The occurrence and the number of short-circuited turns are predicted using support-vector machine as a classifier. The classification results indicate that the introduced criterion can detect the short-circuit fault incisively. Simulation results are verified by the experimental results.