Showing papers on "White noise published in 1992"

Discrete Random Signals and Statistical Signal Processing

Abstract: Random vectors random processes moment analysis linear transformations estimation optimal filtering linear prediction linear models spectrum estimation.

Detection, Estimation, and Modulation Theory : Radar-Sonar Signal Processing and Gaussian Signals in Noise

Abstract: Book on detection, estimation and modulation theory, Part 3, Gaussian and radar-sonar signals in noise, covering point targets, random process and scatter channels

Estimation of fractal signals from noisy measurements using wavelets

Abstract: The role of the wavelet transformation as a whitening filter for 1/f processes is exploited to address problems of parameter and signal estimations for 1/f processes embedded in white background noise. Robust, computationally efficient, and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood, and Cramer-Rao bounds are obtained. Included among these algorithms are optimal fractal dimension estimators for noisy data. Algorithms for obtaining Bayesian minimum-mean-square signal estimates are also derived together with an explicit formula for the resulting error. These smoothing algorithms find application in signal enhancement and restoration. The parameter estimation algorithms find application in signal enhancement and restoration. The parameter estimation algorithms, in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process, are useful in problems of signal detection and classification. Results from simulations are presented to demonstrated the viability of the algorithms. >

Stochastic Runge-Kutta algorithms. I. White noise

Abstract: A higher-order algorithm for the numerical integration of one-variable, additive, white-noise equations is developed. The method of development is to extend standard deterministic Runge-Kutta algorithms to include stochastic terms. The ability of the algorithm to generate proper correlation properties is tested on the Ornstein-Uhlenbeck process, showing higher accuracy even with longer step size.

Speech bandwidth extension method and apparatus

Abstract: A speech bandwidth extension method and apparatus analyzes narrowband speech sampled at 8 kHz using LPC analysis to determine its spectral shape and inverse filtering to extract its excitation signal. The excitation signal is interpolated to a sampling rate of 16 kHz and analyzed for pitch control and power level. A white noise generated wideband signal is then filtered to provide a synthesized wideband excitation signal. The narrowband shape is determined and compared to templates in respective vector quantizer codebooks, to select respective highband shape and gain. The synthesized wideband excitation signal is then filtered to provide a highband signal which is, in turn, added to the narrowband signal, interpolated to the 16 kHz sample rate, to produce an artificial wideband signal. The apparatus may be implemented on a digital signal processor chip.

Subspace model identification Part 2. Analysis of the elementary output-error state-space model identification algorithm

Abstract: The elementary MOESP algorithm presented in the first part of this series of papers is analysed in this paper. This is done in three different ways. First, we study the asymptotic properties of the estimated state-space model when only considering zero-mean white noise perturbations on the output sequence. It is shown that, in this case, the MOESPl implementation yields asymptotically unbiased estimates. An important constraint to this result is that the underlying system must have a finite impulse response and subsequently the size of the Hankel matrices, constructed from the input and output data at the beginning of the computations, depends on the number of non-zero Markov parameters. This analysis, however, leads to a second implementation of the elementary MOESP scheme, namely MOESP2. The latter implementation has the same asymptotic properties without the finite impulse response constraint. Secondly, we compare the MOESP2 algorithm with a classical state space model identification scheme. The latter...

A Bayesian estimation approach for speech enhancement using hidden Markov models

Abstract: A Bayesian estimation approach for enhancing speech signals which have been degraded by statistically independent additive noise is motivated and developed. In particular, minimum mean square error (MMSE) and maximum a posteriori (MAP) signal estimators are developed using hidden Markov models (HMMs) for the clean signal and the noise process. It is shown that the MMSE estimator comprises a weighted sum of conditional mean estimators for the composite states of the noisy signal, where the weights equal the posterior probabilities of the composite states given the noisy signal. The estimation of several spectral functionals of the clean signal such as the sample spectrum and the complex exponential of the phase is also considered. A gain-adapted MAP estimator is developed using the expectation-maximization algorithm. The theoretical performance of the MMSE estimator is discussed, and convergence of the MAP estimator is proved. Both the MMSE and MAP estimators are tested in enhancing speech signals degraded by white Gaussian noise at input signal-to-noise ratios of from 5 to 20 dB. >

Nonlinear prediction as a way of distinguishing chaos from random fractal sequences

Abstract: NONLINEAR forecasting has recently been shown to distinguish between deterministic chaos and uncorrelated (white) noise added to periodic signals1, and can be used to estimate the degree of chaos in the underlying dynamical system2. Distinguishing the more general class of coloured (autocorrelated) noise has proven more difficult because, unlike additive noise, the correlation between predicted and actual values measured may decrease with time—a property synonymous with chaos. Here, we show that by determining the scaling properties of the prediction error as a function of time, we can use nonlinear prediction to distinguish between chaos and random fractal sequences. Random fractal sequences are a particular class of coloured noise which represent stochastic (infinite-dimensional) systems with power-law spectra. Such sequences have been known to fool other procedures for identifying chaotic behaviour in natural time series9, particularly when the data sets are small. The recognition of this type of noise is of practical importance, as measurements from a variety of dynamical systems (such as three-dimensional turbulence, two-dimensional and geostrophic turbulence, internal ocean waves, sandpile models, drifter trajectories in large-scale flows, the motion of a classical electron in a crystal and other low-dimensional systems) may over some range of frequencies exhibit power-law spectra.

Channel modeling and simulation in satellite mobile communication systems

Abstract: An analog model describing signal amplitude and phase variations on shadowed satellite mobile channels is proposed. A linear combination of log-normal, Rayleigh, and Rice models is used to describe signal variations over an area with constant environment attributes while an M-state Markov chain is applied to represent environment parameter variations. Channel parameters are evaluated from the experimental data and utilized to verify a simulation model. Results, presented in the form of signal waveforms, probability density functions, fade durations, and average bit and block error rates, show close agreement with measurements. >

White noise driven quasilinear SPDEs with reflection

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.

A compact Cramer-Rao bound expression for parametric estimation of superimposed signals

Abstract: The problem of parameter estimation of superimposed signals in white Gaussian noise is considered. Closed-form expressions of the Cramer-Rao bound for real or complex signals with vector parameters are derived, extending recent results by P. Stoica and A. Nehorai (1989). >

Errors associated with fitting Gaussian profiles to noisy emission-line spectra

Abstract: Landman et al. (1982) developed prescriptions to predict profile fitting errors for Gaussian emission lines perturbed by white noise. We show that their scaling laws can be generalized to more complicated signal-dependent 'noise models' of common astronomical detector systems.

Renormalization Exponents and Optimal Pointwise Rates of Convergence

Abstract: Simple renormalization arguments can often be used to calculate optimal rates of convergence for estimating linear functionals from indirect measurements contaminated with white noise. This allows one to quickly identify optimal rates for certain problems of density estimation, nonparametric regression, signal recovery and tomography. Optimal kernels may also be derived from renormalization; we give examples for deconvolution and tomography.

Generalization in a linear perceptron in the presence of noise

Abstract: The authors study the evolution of the generalization ability of a simple linear perceptron with N inputs which learns to imitate a 'teacher perceptron'. The system is trained on p= alpha N example inputs drawn from some distribution and the generalization ability is measured by the average agreement with the teacher on test examples drawn from the same distribution. The dynamics may be solved analytically and exhibits a phase transition from imperfect to perfect generalization at alpha =1, when there are no errors (static noise) in the training examples. If the examples are produced by an erroneous teacher, overfitting is observed, i.e. the generalization error starts to increase after a finite time of training. It is shown that a weight decay of the same size as the variance of the noise (errors) on the teacher improves on the generalization and suppresses the overfitting. The generalization error as a function of time is calculated numerically for various values of the parameters. Finally dynamic noise in the training is considered. White noise on the input corresponds on average to a weight decay, and can thus improve generalization, whereas white noise on the weights or the output degrades generalization. Generalization is particularly sensitive to noise on the weights (for alpha (1) where it makes the error constantly increase with time, but this effect is also shown to be damped by a weight decay. Weight noise and output noise acts similarly above the transition at alpha =1.

Achievable information rates on digital subscriber loops: limiting information rates with crosstalk noise

Abstract: The capacity and cutoff rates for channels with linear intersymbol interference, power dependent crosstalk noise, and additive white noise are examined, focusing on high speed digital subscriber line data transmission. The effects of varying the level of additive white noise, crosstalk coupling gain, sampling rate, and input power levels are studied in detail for a set of simulated two-wire local loops. A closed-form expression for the shell constrained Gaussian cutoff rate on the crosstalk limited channel is developed and related to the capacity, showing that the relationship between these two rates is the same as on a channel without crosstalk noise. The study also projects achievable rates on a digital subscriber line, inside and outside of a carrier serving area, with a sophisticated but realizable receiver. >

Detection and localization of multiple sources in noise with unknown covariance

Abstract: The authors present a novel technique for the detection and localization of multiple sources in the presence of noise with unknown and arbitrary covariance. The technique is applicable to coherent and noncoherent signals and to arbitrary array geometry and is based on Rissanen's minimum description length (MDL) principle (1989) for model selection. Its computational load is comparable to that of analogous techniques for white noise. Simulation results demonstrating the performance of this technique are included. >

A unified approach to the design of linear constraints in minimum variance adaptive beamformers

Abstract: A simple, systematic procedure for designing linear constraints in minimum-variance beamformers which allows an arbitrary specification of the quiescent response (the beamformer response when only white noise is present) is described. In this approach, the first constraint is dedicated to the imposition of a desired quiescent response, and additional constraints are included to assure proper reception of the desired signal. These additional constraints make the overall beamformer response equal to the quiescent response in the desired signal region so that the signal is not cancelled when it is present. Optionally, the response can be fixed in other regions of interest by adding more constraints. This design procedure demonstrates that the key to designing efficient constraints is finding the weighting coefficients which specify the desired quiescent response, a problem identical to the synthesis of desired beam patterns for nonadaptive arrays. The effectiveness of the procedure is illustrated by examples in both narrowband and broadband arrays. >

Estimating Model-Error Covariances for Application to Atmospheric Data Assimilation

Abstract: Forecast-error statistics have traditionally been used to investigate model performance and to calculate analysis weights for atmospheric data assimilation. Forecast error has two components: the model error, caused by model imperfections, and the predictability error, which is due to the model generation of instabilities from an imperfectly defined initial state. Traditionally, these two error sources have been difficult to separate. The Kalman filter theory assumes that the model error is additive white (in time) noise, which permits the separation of the model and predictability error. Progress can be made by assuming that the model-error statistics are homogeneous and stationary, an assumption that is more justifiable for the model-error statistics than for the forcast-error statistics. A methodology for estimating the homogeneous, stationary component of the model- error covariance is discussed and tested in a simple data-assimilation system.

Infinite-dimensional rotations and Laplacians in terms of white noise calculus

Abstract: The theory of generalized white noise functionals (white noise calculus) initiated in [2] has been considerably developed in recent years, in particular, toward applications to quantum physics, see e.g. [5], [7] and references cited therein. On the other hand, since H. Yoshizawa [4], [23] discussed an infinite dimensional rotation group to broaden the scope of an investigation of Brownian motion, there have been some attempts to introduce an idea of group theory into the white noise calculus. For example, conformal invariance of Brownian motion with multidimensional parameter space [6], variational calculus of white noise functionals [14], characterization of the Levy Laplacian [17] and so on.

A new approximate solution technique for randomly excited non-linear oscillators—II

Abstract: The method of weighted residuals is applied to the reduced Fokker-Planck equation associated with a non-linear oscillator, which is subjected to both additive and multiplicative Gaussian white noise excitations. A set of constraints are deduced for obtaining an approximate stationary probability density for the system response. One of the constraints coincides with the previously proposed criterion of dissipation energy balancing, and the others are useful for calculating the equivalent conservative force. It is shown that these constraints imply certain relationships among certain statistical moments; their imposition guarantees that such moments computed from the approximate probability density satisfy the corresponding exact equations derived from the original equation of motion. Moreover, the well-known procedure of stochastic linearization and its improved version of partial linearization are shown to be special cases of this scheme, and they are less accurate since the approximations are not chosen from the entire set of the solution pool of generalized stationary potential. Applications of the scheme are illustrated by examples, and its accuracy is substantiated by Monte Carlo simulation results.

Deterministic 1/f noise in nonconserative models of self-organized criticality.

Abstract: Generic, deterministic, nonconservative models displaying self-organized criticality are shown to exhibit 1/{ital f} noise. The exponent of the power spectrum depends on the level of conservation.

Using the correlation exponent to decide whether an economic series is chaotic

Abstract: We consider two ways of distinguishing deterministic time-series from stochastic white noise; the Grassberger—Procaccia correlation exponent test and the Brock, Dechert, Scheinkman (or BDS) test. Using simulated data to test the power of these tests, the correlation exponent test can distinguish white noise from chaos. It cannot distinguish white noise from chaos mixed with a small amount of white noise. With i.i.d. as the null, the BDS correctly rejects the null when the data are deterministic chaos. Although the BDS test may also reject the null even when the data are stochastic, it may be useful in distinguishing between linear and nonlinear stochastic processes.

Response Statistics of Nonlinear Dynamic Systems by Path Integration

Abstract: The paper presents a method for calculating the response statistics of nonlinear dynamic systems excited by a white noise or filtered white noise process. The method, which is based on the path integral solution technique, is still under development, but experience so far indicates that it is singularly well suited for numerical calculation of the response statistics of nonlinear systems to which can be associated a Markov vector process whose probability density satisfies a Fokker-Planck-Kolmogorov (FPK) equation. The method is a viable alternative to the direct numerical solution of the FPK equation. A key feature of the method is the possibility of obtaining highly accurate solutions at very low probability levels. Also, there seems to be almost no limitation on the type of nonlinearity that can be accomodated. On the negative side there are clear limitations of the method concerning required computer resources.

Optimal stabilizing compensator for linear systems with state-dependent noise

Abstract: Results concerning construction of an optimal stabilizing compensator are obtained for the case of state-dependent white noise

Physical basis for a time series model of soil water content

Abstract: A first-order autoregressive Markovian model AR(1) is formulated on the basis of the hydrologic budget and soil water transport equation. The model predictions compared well with neutron probe measurements of soil moisture content, and the statistical moments were conserved. The applied water events were white noise in structure, and the random shocks generated from the flow dynamics simplifications have a statistical mean of zero and were uncorrelated for all time lags. The derived AR(1) model parameter is used to compute the mean diffusivity of the soil, which is in agreement with reported lab measurements and field estimates obtained from cumulative evaporation measurements made with two large lysimeters.