Showing papers on "White noise published in 2000"

Optical encryption by double-random phase encoding in the fractional Fourier domain.

Abstract: We propose an optical architecture that encodes a primary image to stationary white noise by using two statistically independent random phase codes. The encoding is done in the fractional Fourier domain. The optical distribution in any two planes of a quadratic phase system (QPS) are related by fractional Fourier transform of the appropriately scaled distribution in the two input planes. Thus a QPS offers a continuum of planes in which encoding can be done. The six parameters that characterize the QPS in addition to the random phase codes form the key to the encrypted image. The proposed method has an enhanced security value compared with earlier methods. Experimental results in support of the proposed idea are presented.

On timing offset estimation for OFDM systems

Abstract: Two timing offset estimation methods for orthogonal frequency division multiplexing (OFDM) systems as modifications to Schmidl and Cox's method (see IEEE Trans. Commun., vol.45, p.1613-21, 1997) are presented. The performances of the timing offset estimators in additive white Gaussian noise channel and intersymbol interference channel are compared in terms of estimator variance obtained by simulation. Both proposed methods have significantly smaller estimator variance in both channel conditions.

Fractional market dynamics

Abstract: A new extension of a fractality concept in nancial mathematics has been developed. We have introduced a new fractional Langevin-type stochastic dierential equation that diers from the standard Langevin equation: (i) by replacing the rst-order derivative with respect to time by the fractional derivative of order ; and (ii) by replacing \white noise" Gaussian stochastic force by the generalized \shot noise", each pulse of which has a random amplitude with the -stable Levy distribution. As an application of the developed fractional non-Gaussian dynamical approach the expression for the probability distribution function (pdf) of the returns has been established. It is shown that the obtained fractional pdf ts well the central part and the tails of the empirical distribution of S&P 500 returns. c 2000 Elsevier Science B.V. All rights reserved.

Estimation and detection of event-related fMRI signals with temporally correlated noise: a statistically efficient and unbiased approach.

Abstract: Recent developments in analysis methods for event-related functional magnetic resonance imaging (fMRI) has enabled a wide range of novel experimental designs. As with selective averaging methods used in event-related potential (ERP) research, these methods allow for the estimation of the average time-locked response to particular event-types, even when these events occur in rapid succession and in an arbitrary sequence. Here we present a flexible framework for obtaining efficient and unbiased estimates of event-related hemodynamic responses, in the presence of realistic temporally correlated (nonwhite) noise. We further present statistical inference methods based upon the estimated responses, using restriction matrices to formulate temporal hypothesis tests about the shape of the evoked responses. The accuracy of the methods is assessed using synthetic noise, actual fMRI noise, and synthetic activation in actual noise. Actual false-positive rates were compared to nominal false-positive rates assuming white noise, as well as local and global noise estimates in the estimation procedure (assuming white noise resulted in inappropriate inference, while both global and local estimates corrected false-positive rates). Furthermore, both local and global noise estimates were found to increase the statistical power of the hypothesis tests, as measured by the receiver operating characteristics (ROC). This approach thus enables appropriate univariate statistical inference with improved statistical power, without requiring a priori assumptions about the shape or timing of the event-related hemodynamic response.

Quantile based noise estimation for spectral subtraction and Wiener filtering

Abstract: Elimination of additive noise from a speech signal is a fundamental problem in audio signal processing. In this paper we restrict our considerations to the case where only a single microphone recording of the noisy signal is available. The algorithms which we investigate proceed in two steps. First, the noise power spectrum is estimated. A method based on temporal quantiles in the power spectral domain is proposed and compared with pause detection and recursive averaging. The second step is to eliminate the estimated noise from the observed signal by spectral subtraction or Wiener filtering. The database used in the experiments comprises 6034 utterances of German digits and digit strings by 770 speakers in 10 different cars. Without noise reduction, we obtain an error rate of 11.7%. Quantile based noise estimation and Wiener filtering reduce the error rate to 8.6%. Similar improvements are achieved in an experiment with artificial, non-stationary noise.

Double random fractional Fourier domain encoding for optical security

Abstract: We propose a new optical encryption technique using the fractional Fourier transform. In this method, the data are encrypted to a stationary white noise by two statistically independent random phase masks in fractional Fourier domains. To decrypt the data correctly, one needs to specify the fractional domains in which the input plane, encryp- tion plane, and output planes exist, in addition to the key used for en- cryption. The use of an anamorphic fractional Fourier transform for the encryption of two-dimensional data is also discussed. We suggest an optical implementation of the proposed idea. Results of a numerical simulation to analyze the performance of the proposed method are pre- sented. © 2000 Society of Photo-Optical Instrumentation Engineers. (S0091-3286(00)01811-0)

Tests of common stochastic trends

Abstract: This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is derived for the general model. The test is then extended to deal with a serially correlated stationary component. The main contribution of the paper is to propose a test of the validity of a specified value for the rank of the covariance matrix of the disturbances driving the multivariate random walk. This rank is equal to the number of common trends, or levels, in the series. The test is very simple insofar as it does not require any models to be estimated, even if serial correlation is present. Its use with real data is illustrated in the context of a stochastic volatility model, and the relationship with tests in the cointegration literature is discussed.

Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

Abstract: Many approaches have been studied for the array processing problem when the additive noise is modeled with a Gaussian distribution, but these schemes typically perform poorly when the noise is non-Gaussian and/or impulsive. This paper is concerned with maximum likelihood array processing in non-Gaussian noise. We present the Cramer-Rao bound on the variance of angle-of-arrival estimates for arbitrary additive, independent, identically distributed (iid), symmetric, non-Gaussian noise. Then, we focus on non-Gaussian noise modeling with a finite Gaussian mixture distribution, which is capable of representing a broad class of non-Gaussian distributions that include heavy tailed, impulsive cases arising in wireless communications and other applications. Based on the Gaussian mixture model, we develop an expectation-maximization (EM) algorithm for estimating the source locations, the signal waveforms, and the noise distribution parameters. The important problems of detecting the number of sources and obtaining initial parameter estimates for the iterative EM algorithm are discussed in detail. The initialization procedure by itself is an effective algorithm for array processing in impulsive noise. Novel features of the EM algorithm and the associated maximum likelihood formulation include a nonlinear beamformer that separates multiple source signals in non-Gaussian noise and a robust covariance matrix estimate that suppresses impulsive noise while also performing a model-based interpolation to restore the low-rank signal subspace. The EM approach yields improvement over initial robust estimates and is valid for a wide SNR range. The results are also robust to PDF model mismatch and work well with infinite variance cases such as the symmetric stable distributions. Simulations confirm the optimality of the EM estimation procedure in a variety of cases, including a multiuser communications scenario. We also compare with existing array processing algorithms for non-Gaussian noise.

Coherence and stochastic resonance in a two-state system

Abstract: The subject of our study is a two-state dynamics driven by Gaussian white noise and a weak harmonic signal. The system resulting from a piecewise linear FizHugh-Nagumo model in the case of perfect time scale separation between fast and slow variables shows either bistable, excitable, or oscillatory behavior. Its output spectra as well as the spectral power amplification of the signal can be calculated for arbitrary noise strength and frequency, allowing characterization of the coherence resonance in the bistable and excitable regimes as well as quantification of nonadiabatic resonances with respect to the external signal in all regimes.

Biomedical Signal Processing and Signal Modeling

Abstract: The Nature of Biomedical Signals. Memory and Correlation. The Impulse Response. Frequency Response. Modeling Continuous-Time Signals as Sums of Sine Waves. Responses of Linear Continuous-Time Filters to Arbitrary Inputs. Modeling Signals as Sums of Discrete-Time Sine Waves. Noise Removal and Signal Compensation. Modeling Stochastic Signals as Filtered White Noise. Scaling and Long-Term Memory. Nonlinear Models of Signals. Assessing Stationarity and Reproducibility. Appendix.

Blind separation of nonstationary sources in noisy mixtures

Abstract: A new method of blind source separation is presented that is not sensitive to additive white noise. The method exploits the nonstationarity and temporal structure of sources. The method only requires multiple time-delayed correlation matrices of the observed data at several different time-windowed data frames to estimate the mixing matrix. The implementation using joint diagonalisation (JD) is described. Simulations verify the high performance of the proposed method, especially in a low SNR environment.

Extended theory of early-late code tracking for a bandlimited gps receiver

Abstract: Code-tracking accuracy, an important attribute of GPS receivers, depends both on characteristics of the signal being tracked and on the design of the receiver. A simple expression has been available to predict code-tracking accuracy for early-late processing of signals with sinc-squared spectra in white noise for an infinite front-end bandwidth receiver. However, the literature has not indicated when this approximation holds. This paper provides a more exact analysis of code-tracking accuracy for early-late discriminators processing conven-tional binary phase shift keyed signals in white noise. New analytical expressions apply for various front-end bandwidths, discriminator spacings, and code-tracking loop bandwidths, while using linear models based on a small-error assumption. A theoretical lower bound is also supplied, indicating inherent limits on accuracy for given conditions. While evaluation of the exact expressions requires numerical integrations, new algebraic approximations are also provided. Numerical results compare the various expressions and approximations.

Comparison of current-driven and conductance-driven neocortical model neurons with Hodgkin-Huxley voltage-gated channels.

Abstract: Intrinsic noise and random synaptic inputs generate a fluctuating current across neuron membranes. We determine the statistics of the output spike train of a biophysical model neuron as a function of the mean and variance of the fluctuating current, when the current is white noise, or when it derives from Poisson trains of excitatory and inhibitory postsynaptic conductances. In the first case, the firing rate increases with increasing variance of the current, whereas in the latter case it decreases. In contrast, the firing rate is independent of variance (for constant mean) in the commonly used random walk, and perfect integrate-and-fire models for spike generation. The model neuron can be in the current-dominated state, representative of neurons in the in vitro slice preparation, or in the fluctuation-dominated state, representative of in vivo neurons. We discuss the functional relevance of these states to cortical information processing.

Extinction risk under coloured environmental noise

Abstract: Positively autocorrelated red environmental noise is characterized by a strong dependence of expected sample variance on sample length. This dependence has to be taken into account when assessing extinction risk under red and white uncorrelated environmental noise. To facilitate a comparison between red and white noise, their expected variances can be scaled to be equal, but only at a chosen time scale. We show with a simple one-dimensional population dynamics model that the different but equally reasonable choices of the time scale yield qualitatively different results on the dependence of extinction risk on the colour of environmental noise: extinction risk might increase as well as decrease when the temporal correlation of noise increases.

A recursive algorithm for the error probability evaluation of M-QAM

Abstract: A general recursive algorithm for the efficient and accurate computation of the bit error rate (BER) of square-shaped M-QAM constellations over additive white Gaussian noise (AWGN) channels is derived. We take advantage of the relationship amongst different square-shaped M-QAM constellations using Gray coded bit mapping.

Automatic sound detection and recognition for noisy environment

Abstract: This paper addresses the problem of automatic detection and recognition of impulsive sounds, such as glass breaks, human screams, gunshots, explosions or door slams. A complete detection and recognition system is described and evaluated on a sound database containing more than 800 signals distributed among six different classes. Emphasis is set on robust techniques, allowing the use of this system in a noisy environment. The detection algorithm, based on a median filter, features a highly robust performance even under important background noise conditions. In the recognition stage, two statistical classifiers are compared, using Gaussian Mixture Models (GMM) and Hidden Markov Models (HMM), respectively. It can be shown that a rather good recognition rate (98% at 70dB and above 80% for 0dB signal-to-noise ratios) can be reached, even under severe gaussian white noise degradations.

Mean weight behavior of the filtered-X LMS algorithm

Abstract: A new stochastic analysis is presented for the filtered-X LMS (FXLMS) algorithm. The analysis does not use independence theory. An analytical model is derived for the mean behavior of the adaptive weights. The model is valid for white or colored reference inputs and accurately predicts the mean weight behavior even for large step sizes. The constrained Wiener solution is determined as a function of the input statistics and the impulse responses of the adaptation loop filters. Effects of secondary path estimation error are studied. Monte Carlo simulations demonstrate the accuracy of the theoretical model.

Adaptive confidence interval for pointwise curve estimation

Abstract: We present a procedure associated with nonlinear wavelet methods that provides adaptive confidence intervals around $f (x_0)$, in either a white noise model or a regression setting. A suitable modification in the truncation rule for wavelets allows construction of confidence intervals that achieve optimal coverage accuracy up to a logarithmic factor. The procedure does not require knowledge of the regularity of the unknown function $f$; it is also efficient for functions with a low degree of regularity.

Adaptive Bayesian multiuser detection for synchronous CDMA with Gaussian and impulsive noise

Abstract: We consider the problem of simultaneous parameter estimation and data restoration in a synchronous CDMA system in the presence of either additive Gaussian or additive impulsive white noise with unknown parameters. The impulsive noise is modeled by a two-term Gaussian mixture distribution. Bayesian inference of all unknown quantities is made from the superimposed and noisy received signals. The Gibbs sampler (a Markov chain Monte Carlo procedure) is employed to calculate the Bayesian estimates. The basic idea is to generate ergodic random samples from the joint posterior distribution of all unknown and then to average the appropriate samples to obtain the estimates of the unknown quantities. Adaptive Bayesian multiuser detectors based on the Gibbs sampler are derived for both the Gaussian noise synchronous CDMA channel and the impulsive noise synchronous CDMA channel. A salient feature of the proposed adaptive Bayesian multiuser detectors is that they can incorporate the a priori symbol probabilities, and they produce as output the a posteriori symbol probabilities. (That is, they are "soft-input soft-output" algorithms.) Hence, these methods are well suited for iterative processing in a coded system, which allows the adaptive Bayesian multiuser detector to refine its processing based on the information from the decoding stage, and vice versa-a receiver structure termed the adaptive turbo multiuser detector.

A matrix-pencil approach to blind separation of colored nonstationary signals

Abstract: For many signal sources such as speech with distinct, nonwhite power spectral densities, second-order statistics of the received signal mixture can be exploited for signal separation. Without knowledge of the noise correlation matrix, we propose a simple and yet effective signal extraction method for signal source separation under unknown temporally white noise. This new and unbiased signal extractor is derived from the matrix pencil formed between output autocorrelation matrices at different delays. Based on the matrix pencil, an ESPRIT-type algorithm is derived to get an optimal solution in the least square sense. Our method is well suited for systems with colored sensor noises and for nonstationary signals.

A Practical Guide to Model Observers for Visual Detection in Synthetic and Natural Noisy Images

Abstract: When an investigator is developing a new image-processing technique or manipulating an image-acquisition technique they are confronted with the question of whether the new technique will improve clinical diagnosis. A first approach is to look at individual physical properties of the image such as image contrast and resolution. Although these properties might be useful, it has long been known that the noise characteristics of the image system need to be taken into consideration to appropriately evaluate the quality of an image whether it will be used to detect, classify, and/ˆ•or estimate a signal (Cunningham and Shaw, 1999). One useful measure of the noise characteristics is the noise-equivalent quanta (NEQ) that expresses the image noise in terms of the number of Poisson-distributed input photons per unit area at each spatial frequency (Wagner and Brown, 1985). The NEQ can be thought of as a measure inversely related to the amount of noise as a function of spatial frequency. However, when the diagnostic decision involves a human observer, medical image quality can be defined in terms of human performance in visual tasks that are relevant to clinical diagnosis (Barrett, 1993). In this context, receiver operating characteristics (ROC) studies are the standard method of evaluating the impact of a particular image manipulation on clinical diagnosis. In these studies, the physicians scrutinize a set of medical images (under the different image-acquisition or processing conditions) and rate their confidence about the presence of the lesion. The investigator infers from these ratings a measure of performance known as the area under the ROC curve. Often, the number of possible conditions is large and ROC studies become time consuming and costly because they require a large number of human observations. Other times, the investigator might want to optimize a parameter or a set of parameters. In such cases, the number of conditions suffers a combinatorial explosion, and therefore ROC studies become unfeasible. Thus it is desirable to develop a metric of image quality that could be used for fast evaluation and optimization of image quality but also would have the predictive power of ROC studies. Computer-model observers are algorithms that attempt to predict human visual performance in noisy images and might represent the desired metric of image quality when the diagnostic decision involves a human observer and a visual task. Development of models to predict human visual signal detection in noise goes back to work by Rose (1948) who studied the detectability of a flat-topped disk embedded in white noise (see Burgess, 1999a, for a review). In the last two decades, many studies have concentrated on finding a model observer that can predict human performance across many types of synthetic backgrounds. More recently, model observers have been applied to real medical-image backgrounds. The hope is that eventually model observers will become common metrics of task-based image quality for evaluation of medical-image quality as well as optimization of imaging systems.

Chaos communication over noisy channels

Abstract: The problem of transmitting digital information using chaotic signals over a channel with Gaussian white noise perturbation is introduced rigorously. It is shown that discrete time base-band chaotic communication systems with discrete time Gaussian white noise in the channel are sufficiently general in this context. The optimal receiver is given explicitly in terms of conditional probabilities. For the example of chaos shift keying using iterations of the tent map, the optimal classifier is constructed explicitly. Finally, it is shown how previously published methods, in particular those based on chaos synchronization, fit into this framework.

The Response of an ENSO Model to Climate Noise, Weather Noise and Intraseasonal Forcing

Abstract: The response of an intermediate coupled model of the tropical Pacific to different forms of stochastic wind forcing is studied. An estimate of observed Pacific wind variance that is unrelated to Pacific sea surface temperature (SST) has a red spectrum, inconsistent with standard definitions of “weather noise”. The reddening is likely due to SST outside the basin; we propose a definition of “climate noise” for such reddened variance. Effects are compared for (i) red climate noise; (ii) the corresponding white weather noise estimate; (iii) intraseasonal and interannual components of the white noise (to test frequency response); and (iv) a noise product with extra power in the 30–60 day range. Power is not effectively channeled from subannual frequencies to the frequencies associated with ENSO in this model. This suggests that ENSO impacts of the Madden-Julian oscillation are largely restricted to the low-frequency tail rather than the 30–60 day spectral peak. Interannual climate noise originating outside the tropical Pacific appears important.

Using the Allan variance and power spectral density to characterize dc nanovoltmeters

Abstract: When analyzing nanovoltmeter measurements, stochastic serial correlations are often ignored and the experimental standard deviation of the mean is assumed to be the experimental standard deviation of a single observation divided by the square root of the number of observations. This is justified only for white noise. This paper demonstrates the use of the power spectrum and the Allan variance to analyze data, identify the regimes of white noise, and characterize the performance of digital and analog DC nanovoltmeters. Limits imposed by temperature variations, 1/f noise and source resistance are investigated.

Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations

Abstract: We consider adaptive estimating the value of a linear functional from indirect white noise observations. For a flexible approach, the problem is embedded in an abstract Hilbert scale. We develop an adaptive estimator that is rate optimal within a logarithmic factor simultaneously over a wide collection of balls in the Hilbert scale. It is shown that the proposed estimator has the best possible adaptive properties for a wide range of linear functionals. The case of discretized indirect white noise observations is studied, and the adaptive estimator in this setting is developed.

Fractional Langevin Equation to Describe Anomalous Diffusion

Abstract: A Langevin equation with a special type of additive random source is considered. This random force presents a fractional order derivative of white noise, and leads to a power-law time behavior of the mean square displacement of a particle, with the power exponent being noninteger. More general equation containing fractional time differential operators instead of usual ones is also proposed to describe anomalous diffusion processes. Such equation can be regarded as corresponding to systems with incomplete Hamiltonian chaos, and, depending on the type of the relationship between the speed and coordinate of a particle, yields either usual or fractional long-time behavior of diffusion.