White noise

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

On hilbert spectral representation: A true time-frequency representation for nonlinear and nonstationary data

Abstract: As the original definition on Hilbert spectrum was given in terms of total energy and amplitude, there is a mismatch between the Hilbert spectrum and the traditional Fourier spectrum, which is defined in terms of energy density. Rigorous definitions of Hilbert energy and amplitude spectra are given in terms of energy and amplitude density in the time-frequency space. Unlike Fourier spectral analysis, where the resolution is fixed once the data length and sampling rate is given, the time-frequency resolution could be arbitrarily assigned in Hilbert spectral analysis (HSA). Furthermore, HSA could also provide zooming ability for detailed examination of the data in a specific frequency range with all the resolution power. These complications have made the conversion between Hilbert and Fourier spectral results difficult and the conversion formula is elusive until now. We have derived a simple relationship between them in this paper. The conversion factor turns out to be simply the sampling rate for the full resolution cases. In case of zooming, there is another additional multiplicative factor. The conversion factors have been tested in various cases including white noise, delta function, and signals from natural phenomena. With the introduction of this conversion, we can compare HSA and Fourier spectral analysis results quantitatively.

Multidimensional Reaction-Diffusion Equations with White Noise Boundary Perturbations

Abstract: In this paper we study multidimensional stochastic reaction-diffusion equations (SRDE's) with white noise boundary data. More precisely, we consider a general SRDE with Robin data to be a white noise field. Because this boundary data is very irregular, we formulate a set of conditions that a random field must satisfy to solve the SRDE. We show that a unique solution exists, and we study the boundary-layer behavior of the solution. This boundary-layer analysis reveals some natural restrictions on the reaction term of the SRDE that ensure that the reaction term does not qualitatively affect the boundary layer. The boundary-layer analysis also leads to the definition of some functional Banach spaces into which are encoded the boundary-layer degeneracies and that would be the natural settings for other analyses of the SRDE of this paper (e.g., large deviations and central limit theorems, approximation theorems).

Frequency Estimation of Distorted and Noisy Signals in Power Systems by FFT-Based Approach

Abstract: This paper focuses on the accurate frequency estimation of power signals corrupted by a stationary white noise. The noneven item interpolation FFT based on the triangular self-convolution window is described. A simple analytical expression for the variance of noise contribution on the frequency estimation is derived, which shows the variances of frequency estimation are proportional to the energy of the adopted window. Based on the proposed method, the noise level of the measurement channel can be estimated, and optimal parameters (e.g., sampling frequency and window length) of the interpolation FFT algorithm that minimize the variances of frequency estimation can thus be determined. The application in a power quality analyzer verified the usefulness of the proposed method.

New Fast Optimal White-Noise Estimators for Deconvolution

Abstract: We present a brief qualitative discussion of Kalman filtering as contrasted with Wiener filtering, since the Kalman filter is an integral element in our new fast optimal white-noise estimators. Additionally, we present two fast algorithms, one of which is shown to be very efficient for calculating fixed-interval estimates of the reflection coefficient sequence, the other of which is shown to be very efficient for calculating either fixed-point or fixed-lag estimates of that sequence. Detailed operation counts are given which support these claims. Flow charts are also given for the Kalman filter and the two new fast smoothing algorithms.

An approach via fractional analysis to non-linearity induced by coarse-graining in space

Abstract: Loosely speaking, a coarse-grained space is a space in which the generic point is not infinitely thin, but rather has a thickness; and here this feature is modelled as a space in which the generic increment is not d x , but rather ( d x ) α , 0 α 1 . The purpose of the article is to analyse the non-linearity induced by this coarse-graining effect. This approach via ( d x ) α leads us to the use of fractional analysis which thus provides models in the form of nonlinear differential equations of fractional order. Two illustrative examples are considered. In the first one, one shows that a particle which has a Gaussian white noise in a coarse-grained spaces exhibits a trajectory which looks like a generalised fractional Brownian motion. The second example shows how a simple one-dimensional linear dynamics is converted into a non-linear system of fractional order.