Showing papers on "White noise published in 2002"
07 Aug 2002
TL;DR: This analysis is developed to the case of a signal with random (Rayleigh, Rice, Nakagami, and other) amplitude and the distribution of a decision statistic of an energy detector is retrieved and expressions for detection probability are obtained.
Abstract: Urkowitz (1967) has discussed the detection of a deterministic signal of unknown structure in the presence of band-limited Gaussian noise. That analysis is developed to the case of a signal with random (Rayleigh, Rice, Nakagami, and other) amplitude. For such amplitude the distribution of a decision statistic of an energy detector is retrieved and expressions for detection probability are obtained.
442 citations
TL;DR: Simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.
Abstract: A generalized singular value decomposition (GSVD) based algorithm is proposed for enhancing multimicrophone speech signals degraded by additive colored noise. This GSVD-based multimicrophone algorithm can be considered to be an extension of the single-microphone signal subspace algorithms for enhancing noisy speech signals and amounts to a specific optimal filtering problem when the desired response signal cannot be observed. The optimal filter can be written as a function of the generalized singular vectors and singular values of a speech and noise data matrix. A number of symmetry properties are derived for the single-microphone and multimicrophone optimal filter, which are valid for the white noise case as well as for the colored noise case. In addition, the averaging step of some single-microphone signal subspace algorithms is examined, leading to the conclusion that this averaging operation is unnecessary and even suboptimal. For simple situations, where we consider localized sources and no multipath propagation, the GSVD-based optimal filtering technique exhibits the spatial directivity pattern of a beamformer. When comparing the noise reduction performance for realistic situations, simulations show that the GSVD-based optimal filtering technique has a better performance than standard fixed and adaptive beamforming techniques for all reverberation times and that it is more robust to deviations from the nominal situation, as, e.g., encountered in uncalibrated microphone arrays.
383 citations
TL;DR: A comparison of PCA and ICA revealed significant differences in their treatment of both structured and random noise, while PCA was superior for isolation and removal of random noise.
292 citations
TL;DR: The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonancelike behavior.
Abstract: An atom that couples to two distinct leaky optical cavities is driven by an external optical white noise field. We describe how entanglement between the light fields sustained by two optical cavities arises in such a situation. The entanglement is maximized for intermediate values of the cavity damping rates and the intensity of the white noise field, vanishing both for small and for large values of these parameters and thus exhibiting a stochastic-resonancelike behavior. This example illustrates the possibility of generating entanglement by exclusively incoherent means and sheds new light on the constructive role noise may play in certain tasks of interest for quantum information processing.
290 citations
TL;DR: By using the blind approach, it is shown that all internal variables can be recovered solely based on the output measurements and identification of linear and nonlinear parts can be carried out.
274 citations
TL;DR: In this article, the authors estimate the errors due to observational noise on the recurrence quantification analysis (RQA) based on this estimation, and present ways to minimize these errors.
229 citations
TL;DR: In this paper, the Navier-Stokes equations with periodic boundary conditions perturbed by a space-time white noise were studied and a stationary martingale solution was constructed.
222 citations
TL;DR: This paper considers the case where K messages are transmitted through the network in a point-to-point manner, i.e., each message is encoded by exactly one transmitter and is destined for exactly one receiver.
Abstract: A white Gaussian interference network is a channel with T transmitters and R receivers where the received symbols are linear combinations of the transmitted symbols and white Gaussian noise. This paper considers the case where K messages are transmitted through the network in a point-to-point manner, i.e., each message is encoded by exactly one transmitter and is destined for exactly one receiver. It is further assumed that feedback is available so that each transmitter sees the outputs of the receivers to which it is sending messages. Communication strategies based on the discrete Fourier transform (DFT) are developed that perform well for such networks. For multiple-access channels (K=T, R=1) with equal transmitter powers the strategies achieve the feedback sum-rate capacity if the powers are beyond some threshold. For the same channels with fixed transmitter powers and large K, the achievable sum-rate is approximately (log log K)/2 larger than the sum-rate capacity without feedback. For broadcast channels (T=1, K=R) with strong symmetries, the strategies achieve a monotonically increasing sum-rate with K. For interference channels (K=T=R) with strong interference, the strategies significantly enlarge the no-feedback capacity region by "correlation routing.".
185 citations
TL;DR: A new architecture is proposed that encodes a primary image to white noise based on iterative fractional Fourier transform that can provide additional keys for encryption to make the code more difficult to break.
174 citations
TL;DR: In this article, the effects of 1-bit quantization of the input samples has on the direction-of-arrival (DOA) estimation accuracy are considered, and several estimators for the I-bit estimation are discussed.
Abstract: The effects 1-bit quantization of the input samples has on the direction-of-arrival (DOA) estimation accuracy are considered. The signal model assumes a single stochastic Gaussian point source that is embedded in white Gaussian noise (WGN). The inherent limitations governed by the extreme clipping of the input data are analyzed using the Cramer-Rao bound (CRB) that is derived for a two-sensor array. In addition, several estimators for the I-bit estimation are discussed. Numerical and analytical analyses of the estimation error reveal weak dependency on signal-to-noise ratio (SNR) with singular behavior of the estimation error in certain DOA angles.
159 citations
TL;DR: It is shown that the coherence minimization at moderate noise results in a flat spectral response with respect to periodic stimulation in contrast to sharp resonances that are observed for both small and large noise intensities.
Abstract: We study noise-induced resonance effects in the leaky integrate-and-fire neuron model with absolute refractory period, driven by a Gaussian white noise. It is demonstrated that a finite noise level may either maximize or minimize the regularity of the spike train. We also partition the parameter space into regimes where either or both of these effects occur. It is shown that the coherence minimization at moderate noise results in a flat spectral response with respect to periodic stimulation in contrast to sharp resonances that are observed for both small and large noise intensities.
TL;DR: In this paper, a stochastic differential equation (SDE) is used to describe stationary "fluid" random evolutions with independent increments, and it is shown that 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.
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.
TL;DR: In this paper, the authors consider parabolic stochastic partial differential equations driven by white noise in time and prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions.
Abstract: We consider parabolic stochastic partial differential equations driven by white noise in time. We prove exponential convergence of the transition probabilities towards a unique invariant measure under suitable conditions. These conditions amount essentially to the fact that the equation transmits the noise to all its determining modes. Several examples are investigated, including some where the noise does not act on every determining mode directly.
TL;DR: An efficient method is developed, which can perform unbiased parameter estimation without utilizing a prefilter, which is characterized by attractive features: direct use of the observed data without prefiltering.
Abstract: This paper considers the problem of identifying linear systems, where the input is observed in white noise but the output is observed in colored noise which also includes process disturbances. An efficient method is developed, which can perform unbiased parameter estimation without utilizing a prefilter. The developed method is characterized by attractive features: direct use of the observed data without prefiltering; no need to evaluate autocorrelation functions for the input noise; no need to identify a high-order augmented system; and provision of a direct unbiased estimate of the system parameters without parameter extraction. Computer simulations are presented to illustrate its superior performance, including its significantly reduced computational complexity.
10 Dec 2002
TL;DR: JITTERBUG is presented, a MATLAB-based toolbox for real-time control performance analysis that makes it easy to investigate how the control performance is affected by e.g. delay, jitter, lost samples, aborted computations, and jitter compensation.
Abstract: The paper presents JITTERBUG, a MATLAB-based toolbox for real-time control performance analysis. The control system is described using a number of connected continuous-time and discrete-time linear systems driven by white noise. The control performance is measured by a continuous-time quadratic cost function. A stochastic timing model is used to describe when the different discrete-time systems are updated during the control period. Building different models, the tool makes it easy to investigate how the control performance is affected by e.g. delay, jitter, lost samples, aborted computations, and jitter compensation. Aperiodic and multi-rate controllers may also be studied. The tool is also capable of computing the spectral densities of the different signals in the system.
TL;DR: In this paper, a blind approach to the sampled Hammerstein-Wiener model identification is proposed, where all internal variables can be recovered solely based on the output measurements and identification of linear and nonlinear parts can be carried out No a priori structural knowledge about the input nonlinearity is assumed and no white noise assumption is imposed on the input.
TL;DR: In this article, the performance of spherical wavelets in discriminating between standard inflationary (Gaussian) and non-Gaussian models was investigated and it was shown that the spherical Mexican Hat wavelet is superior to the spherical Haar wavelet in detecting skewness and kurtosis.
Abstract: We investigate the performance of spherical wavelets in discriminating between standard inflationary (Gaussian) and non-Gaussian models. For the latter we consider small perturbations of the Gaussian model in which an artificially specified skewness or kurtosis is introduced through the Edgeworth expansion. By combining all the information present in all the wavelet scales with the Fisher discriminant, we find that the spherical Mexican Hat wavelets are clearly superior to the spherical Haar wavelets. The former can detect levels of skewness and kurtosis of ≈1 per cent for 33-arcmin resolution, an order of magnitude smaller than the latter. Also, as expected, both wavelets are better for discriminating between the models than the direct consideration of moments of the temperature maps. The introduction of instrumental white noise in the maps, S/N = 1, does not change the main results of this paper.
TL;DR: The most frequently used types of correlation functions are summarized and reviewed in this paper, together with an explanation of the physical meaning of their parameters, and the corresponding elliptically anisotropic correlation functions can simply be obtained by linear coordinate transforms.
Abstract: — In geophysics, the correlation functions of random media are of principal importance for understanding and inverting the properties of seismic waves propagating in geological structures. Unfortunately, the kinds of correlation functions inappropriate for the description of geological structures are often assumed and applied. The most frequently used types of correlation functions are thus summarized and reviewed in this paper, together with an explanation of the physical meaning of their parameters.¶A stationary random medium is assumed to be realized in terms of a white noise filtered by a spectral filter. The spectral filter is considered isotropic, in a simple general form enabling the random media used in geophysics to be specified. The medium correlation functions, corresponding to the individual special cases of the general random medium (Gaussian, exponential, von Karman, self-affine, Kummer), are then derived and briefly discussed. The corresponding elliptically anisotropic correlation functions can simply be obtained by linear coordinate transforms.
TL;DR: In this article, the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes was considered.
Abstract: We consider the Navier-Stokes equation on a two dimensional torus with a random force which is white noise in time, and excites only a finite number of modes. The number of excited modes depends on the viscosity ν, and grows like ν
-3
when ν goes to zero. We prove that this Markov process has a unique invariant measure and is exponentially mixing in time.
Book•
29 Apr 2002
TL;DR: Signals Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise Signal Characteristics of Signals at the Generalization Detector Output under under the Stochastic Distribution Law of the Signal Probability Distribution Density.
Abstract: PROBABILITY AND STATISTICS Probability: Basic Concepts Random Variables Stochastic Processes Correlation Function Spectral Density Statistical Characteristics Conclusions References CLASSICAL AND MODERN APPROACHES TO SIGNAL DETECTION THEORY Gaussian Approach Markov Approach Bayes' Decision-Making Rule Unbiased and Invariant Decision-Making Rules Mini-Max Decision-Making Rule Sequential Signal Detection Signal Detection in Non-Gaussian Noise Non-Parametric Signal Detection Conclusions References MAIN CHARACTERISTICS OF MULTIPLICATIVE NOISE Classification of the Noise and Interference Sources of the Multiplicative Noise Classification and Main Properties of Multiplicative Noise Correlation Function and Energy Spectrum of Multiplicative Noise Generalized Statistical Model of Multiplicative Noise Conclusions References STATISTICAL CHARACTERISTICS OF SIGNALS UNDER THE STIMULUS OF MULTIPLICATIVE NOISE Deterministic and Quasideterministic Multiplicative Noise Stationary Fluctuating Multiplicative Noise Ensemble and Individual Realizations of the Signal Probability Distribution Density of the Signal in the Additive Gaussian Noise under the Stimulus of Multiplicative Noise Multivariate Probability Distribution Density of Instantaneous Values of the Signal under the Stimulus of Fluctuating Multiplicative Noise Conclusions References MAIN THEORETICAL PRINCIPLES OF THE GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE Basic Concepts Criticism Initial Premises Likelihood Ratio Engineering Interpretation Generalized Detector Distribution Law Conclusions References GENERALIZED APPROACH TO SIGNAL PROCESSING UNDER THE STIMULUS OF MULTIPLICATIVE NOISE AND LINEAR SYSTEMS Signal Characteristics at the Output of Linear System of the Generalized Detector under the Stimulus of Multiplicative Noise Signal Characteristics at the Generalized Detector Output under under the Stimulus of Multiplicative Noise Signal Noise Component for Some Types of Signals Signal Noise Component under the Stimulus of the Slow and Rapid Multiplicative Noise Signal Distribution Law under the Stimulus of Multiplicative Noise Conclusions References GENERALIZED APPROACH TO SIGNAL DETECTION IN THE PRESENCE OF MULTIPLICATIVE AND ADDITIVE GAUSSIAN NOISE Statistical Characteristics of Signals at the Output of the Generalized Detector Detection Performances of the Generalized Detector Known Correlation Function of the Multiplicative Noise One-Channel Generalized Detector Diversity Signal Detection Conclusions References SIGNAL PARAMETER MEASUREMENT PRECISION A Single Signal Parameter Measurement under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise Simultaneous Measurement of Two Signal Parameters under a Combined Stimulus of Weak Multiplicative and Additive Gaussian Noise A Single Parameter Measurement under a Combined Stimulus of High Multiplicative and Additive Gaussian Noise Conclusions References SIGNAL RESOLUTION UNDER THE GENERALIZED APPROACH TO SIGNAL PROCESSING IN THE PRESENCE OF NOISE Estimation Criteria of Signal Resolution Signal Resolution by Woodward Criterion Statistical Criterion of Signal Resolution Conclusions References APPENDIX I: Delta Function APPENDIX II: Correlation Function and Energy Spectrum of Noise Modulation Function NOTATION INDEX INDEX
TL;DR: In this article, it is shown how the relations of the renormalized squared white noise defined by Accardi, Lu, and Volovich [ALV99] can be realized as factorizable current representations or Levy processes on the real Lie algebra??2.
Abstract: It is shown how the relations of the renormalized squared white noise defined by Accardi, Lu, and Volovich [ALV99] can be realized as factorizable current representations or Levy processes on the real Lie algebra ??2. This allows to obtain its Ito table, which turns out to be infinite-dimensional. The linear white noise without or with number operator is shown to be a Levy process on the Heisenberg–Weyl Lie algebra or the oscillator Lie algebra. Furthermore, a joint realization of the linear and quadratic white noise relations is constructed, but it is proved that no such realizations exist with a vacuum that is an eigenvector of the central element and the annihilator. Classical Levy processes are shown to arise as components of Levy processes on real Lie algebras and their distributions are characterized. In particular the square of white noise analogue of the quantum Poisson
process is shown to have a χ2 probability density and the analogue of the field operators to have a density proportional to , where Γ is the usual Γ-function and m
0 a real parameter.
TL;DR: In this article, the impact of 1/f noise and white noise in oscillators and frequency dividers on jitter in phase-locked loops of first-and second-order was analyzed.
Abstract: Jitter in clock signals is analyzed, linking noise in free-running oscillators to short-term and long-term time-domain behavior of phase-locked loops. Particular attention is given to comparing the impact of 1/f noise and white noise in oscillators and frequency dividers on jitter in phase-locked loops of first- and second-order. Theoretical analysis is supported by results obtained using mixed-signal behavior simulation.
01 Aug 2002
TL;DR: A method of blind source separation that jointly exploits the nonstationarity and temporal structure of sources that is insensitive to the temporally white noise and is applicable to the case of either nonstationary sources or temporally correlated sources is addressed.
Abstract: This paper addresses a method of blind source separation that jointly exploits the nonstationarity and temporal structure of sources. The method needs only multiple time-delayed correlation matrices of the observation data, each of which is evaluated at different time-windowed data frame, to estimate the demixing matrix. The method is insensitive to the temporally white noise since it is based on only time-delayed correlation matrices (with non-zero time-lags) and is applicable to the case of either nonstationary sources or temporally correlated sources. We also discuss the extension of some existing methods with the overview of second-order blind source separation methods. Extensive numerical experiments confirm the validity and high performance of the proposed method.
TL;DR: In this paper, a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process.
Abstract: [1] We consider the problem of testing for homogeneity of variance in a time series with long memorystructure.Wedemonstratethat atest whose nullhypothesis isdesigned tobewhite noisecan, in fact, be applied, on a scale by scale basis, to the discrete wavelet transform of long memory processes. In particular, we show that evaluating a normalized cumulative sum of squares test statistic using critical levels for the null hypothesis of white noise yields approximately the same null hypothesis rejection rates when applied to the discrete wavelet transform of samples from a fractionally differenced process. The point at which the test statistic, using a nondecimated version of the discrete wavelet transform, achieves its maximum value can be used to estimate the time of the unknown variance change. We apply our proposed test statistic on five time series derived from the historical record of Nile River yearly minimum water levels covering 622–1922 A.D., each series exhibiting various degrees of serial correlation including long memory. In the longest subseries, spanning 622–1284 A.D., the test confirms an inhomogeneity of variance at short time scales and identifies the change point around 720 A.D., which coincides closely with the construction of a new device around 715 A.D. for measuring the Nile River. The test also detects a change in variance for a record of only 36 years. INDEX TERMS: 1829 Hydrology: Groundwater hydrology; 1869 Hydrology: Stochastic processes; 3299 Mathematical Geophysics: General or miscellaneous;
TL;DR: In this paper, the authors consider linear controlled stochastic systems subjected both to white noise disturbance and Markovian jumping, and derive necessary and sufficient conditions for the zero solution of a linear stochnastic system with multiplicative white noise perturbations.
Abstract: In this paper we consider linear controlled stochastic systems subjected both to white noise disturbance and Markovian jumping. Our aim is to provide a mathematical background in order to give unified approach for a large class of problems associated to linear controlled systems subjected both to multiplicative white noise perturbations and Markovian jumping. First we prove an Ito type formula. Our result extends the result of Ref. [24], to the case when the stochastic process x(t) has not all moments bounded. Necessary and sufficient conditions assuring the exponential stability in mean square for the zero solution of a linear stochastic system with multiplicative white noise and Markovian jumping are provided. Some estimates for solutions of affine stochastic systems are derived, and necessary and sufficient conditions assuring the stochastic stabilizability and stochastic detectability are given. A stochastic version of Bounded Real Lemma is proved and several aspects of the problem of robust stabiliza...
TL;DR: It is shown that the main drawbacks of closure schemes, such as negative values of the PDF in some regions, may be overcome by rewriting the FPK equation in terms of log-probability density function (log-PDF).
TL;DR: In this article, the authors numerically investigate nonlinear Schrodinger equations with a stochastic contribution which is of white noise type and acts either as a potential (multiplicative noise) or as a forcing term (additive noise).
13 May 2002
TL;DR: A new subspace approach is proposed for enhancement of speech corrupted by colored noise based on the simultaneous diagonalization of the clean speech and noise covariance matrices, which leads to an optimal linear estimator that minimizes speech distortion subject to the noise distortion being below a set threshold.
Abstract: A generalized subspace approach is proposed for enhancement of speech corrupted by colored noise. The proposed approach is based on the simultaneous diagonalization of the clean speech and noise covariance matrices, which is shown to be a generalization of the approach proposed by Ephraim and Van Trees for white noise. Objective and subjective measures demonstrated significant improvements over other subspace-based methods when tested with sentences corrupted with speech-shaped noise and multi-talker babble.
TL;DR: The kernel spectral estimation method that is familiar for the classical SSP estimation problem, with the Fourier transform operator and white noise in the observations is extended to incorporate spatial correlation in the data, the system-oriented model of the signal formation operator, and the maximum entropy statistical a priori information about the SSP.
Abstract: The problem of estimating, from one random realization of the remotely sensed signal, the spatial spectrum pattern (SSP) of the wavefield sources distributed in the environment is cast in the framework of Bayesian estimation theory. The kernel spectral estimation method that is familiar, for the classical SSP estimation problem, with the Fourier transform operator and white noise in the observations is extended to incorporate spatial correlation in the data, the system-oriented model of the signal formation operator, and the maximum entropy (ME) statistical a priori information about the SSP. To derive the estimate of the SSP, we applied the Bayesian strategy for maximization of the a posteriori probability density function of the randomized ME model of the SSP. The estimator was obtained as a nonlinear adaptive algorithm that also permits a concise robust implementation. The optimal algorithm implies formation of the second-order sufficient statistics of the data and their smoothing by applying the window operator. The new formalism of the sufficient statistics and windows, explaining their adjustment to the metrics in a solution space, a priori nonparametric model and assumed correlation properties of the desired SSP, is developed. Simulation results are included to illustrate the overall performance of the proposed method in an example of application to radar image formation.
TL;DR: In this article, a weak solution to the stochastic partial differential equation driven by a one sided, α-stable noise without negative jumps is presented. But it is not a Lipschitz function, and is not Gaussian noise.
Abstract: We construct a weak solution to the stochastic partial differential equation driven by a one sided, α-stable noise without negative jumps. We prove the weak existence of the solution for parameters . The facts that, for is not a Lipschitz function, and is not a Gaussian noise require the development of new methods, which we believe are of independent interest. We also show that when the above equation gives an alternative description of super-Brownian motion with stable branching mechanism.