Topic
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, the conditional standard deviation is a piecewise linear function of past values of the white noise, which allows different reactions of the volatility to different signs of the lagged errors.
2,125 citations
2,111 citations
TL;DR: It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint.
Abstract: Adaptive beamforming algorithms can be extremely sensitive to slight errors in array characteristics. Errors which are uncorrelated from sensor to sensor pass through the beamformer like uncorrelated or spatially white noise. Hence, gain against white noise is a measure of robustness. A new algorithm is presented which includes a quadratic inequality constraint on the array gain against uncorrelated noise, while minimizing output power subject to multiple linear equality constraints. It is shown that a simple scaling of the projection of tentative weights, in the subspace orthogonal to the linear constraints, can be used to satisfy the quadratic inequality constraint. Moreover, this scaling is equivalent to a projection onto the quadratic constraint boundary so that the usual favorable properties of projection algorithms apply. This leads to a simple, effective, robust adaptive beamforming algorithm in which all constraints are satisfied exactly at each step and roundoff errors do not accumulate. The algorithm is then extended to the case of a more general quadratic constraint.
1,851 citations
TL;DR: A new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals is developed.
Abstract: Wavelet-based statistical signal processing techniques such as denoising and detection typically model the wavelet coefficients as independent or jointly Gaussian. These models are unrealistic for many real-world signals. We develop a new framework for statistical signal processing based on wavelet-domain hidden Markov models (HMMs) that concisely models the statistical dependencies and non-Gaussian statistics encountered in real-world signals. Wavelet-domain HMMs are designed with the intrinsic properties of the wavelet transform in mind and provide powerful, yet tractable, probabilistic signal models. Efficient expectation maximization algorithms are developed for fitting the HMMs to observational signal data. The new framework is suitable for a wide range of applications, including signal estimation, detection, classification, prediction, and even synthesis. To demonstrate the utility of wavelet-domain HMMs, we develop novel algorithms for signal denoising, classification, and detection.
1,783 citations
TL;DR: In this article, empirical experiments on white noise using the empirical mode decomposition (EMD) method were conducted and it was shown empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components cover the same area on a semi-logarithmic period scale.
Abstract: Based on numerical experiments on white noise using the empirical mode decomposition (EMD) method, we find empirically that the EMD is effectively a dyadic filter, the intrinsic mode function (IMF) components are all normally distributed, and the Fourier spectra of the IMF components are all identical and cover the same area on a semi–logarithmic period scale. Expanding from these empirical findings, we further deduce that the product of the energy density of IMF and its corresponding averaged period is a constant, and that the energy–density function is chi–squared distributed. Furthermore, we derive the energy–density spread function of the IMF components. Through these results, we establish a method of assigning statistical significance of information content for IMF components from any noisy data. Southern Oscillation Index data are used to illustrate the methodology developed here.
1,573 citations