Topic
White noise
About: White noise is a research topic. Over the lifetime, 16496 publications have been published within this topic receiving 318633 citations.
Papers published on a yearly basis
Papers
More filters
82 citations
TL;DR: An efficient likelihood ratio selection (LRS) procedure for identifying the segments is developed, and the asymptotic optimality of this method is presented in the sense that the LRS can separate the signal segments from the noise as long as the signals are in the identifiable regions.
Abstract: Motivated by DNA copy number variation (CNV) analysis based on high-density single nucleotide polymorphism (SNP) data, we consider the problem of detecting and identifying sparse short segments in a long one-dimensional sequence of data with additive Gaussian white noise, where the number, length, and location of the segments are unknown. We present a statistical characterization of the identifiable region of a segment where it is possible to reliably separate the segment from noise. An efficient likelihood ratio selection (LRS) procedure for identifying the segments is developed, and the asymptotic optimality of this method is presented in the sense that the LRS can separate the signal segments from the noise as long as the signal segments are in the identifiable regions. The proposed method is demonstrated with simulations and analysis of a real dataset on identification of copy number variants based on high-density SNP data. The results show that the LRS procedure can yield greater gain in power for de...
82 citations
TL;DR: The algorithm presented here is an optimized REQUEST procedure, which optimally filters measurement as well as propagation noises, in the special case of zero-mean white noises.
Abstract: REQUEST is a recursive algorithm for least-squares estimation of the attitude quaternion of a rigid body using vector measurements. It uses a constant, empirically chosen gain and is, therefore, suboptimal when filtering propagation noises. The algorithm presented here is an optimized REQUEST procedure, which optimally filters measurement as well as propagation noises. The special case of zero-mean white noises is considered. The solution approach is based on state-space modeling of the K-matrix system and uses Kalman-filtering techniques to estimate the optimal K matrix. Then, the attitude quaternion is extracted from the estimated K matrix. A simulation study is used to demonstrate the performance of the algorithm.
82 citations
TL;DR: The paper establishes a theoretical basis for the slow asymptotic convergence and suggests postfiltering as a remedy that would be useful for the full-band LMS AEC and may also be applicable to subband designs.
Abstract: In most acoustic echo canceler (AEC) applications, an adaptive finite impulse response (FIR) filter is employed with coefficients that are computed using the LMS algorithm. The paper establishes a theoretical basis for the slow asymptotic convergence that is often noted in practice for such applications. The analytical approach expresses the mean-square error trajectory in terms of eigenmodes and then applies the asymptotic theory of Toeplitz matrices to obtain a solution that is based on a general characterization of the actual room impulse response. The method leads to good approximations even for a moderate number of taps (N>16) and applies to both full-band and subband designs. Explicit mathematical expressions of the mean-square error convergence are derived for bandlimited white noise, a first-order Markov process, and, more generally, pth-order rational spectra and a direct power-law model, which relates to lowpass FIR filters. These expressions show that the asymptotic convergence is generally slow, being at best of order 1/t for bandlimited white noise. It is argued that input filter design cannot do much to improve slow convergence. However, the theory suggests postfiltering as a remedy that would be useful for the full-band LMS AEC and may also be applicable to subband designs. >
82 citations
TL;DR: The solution of this problem furnishes the kernel of the minimax linear estimate for Gaussian white noise, which is asymptotically minimax among all estimates.
Abstract: We study the problem of estimating an unknown function on the unit interval (or itsk-th derivative), with supremum norm loss, when the function is observed in Gaussian white noise and the unknown function is known only to obey Lipschitz-β smoothness, β>k≧0. We discuss an optimization problem associated with the theory ofoptimal recovery. Although optimal recovery is concerned with deterministic noise chosen by a clever opponent, the solution of this problem furnishes the kernel of the minimax linear estimate for Gaussian white noise. Moreover, this minimax linear estimator is asymptotically minimax among all estimates. We sketch also applications to higher dimensions and to indirect measurement (e.g. deconvolution) problems.
82 citations