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Showing papers on "White noise published in 1999"


Journal ArticleDOI
TL;DR: The CDMA channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods and provides a comparison baseline for CDMA channels with deterministic signature waveforms spanning one symbol period.
Abstract: The CDMA channel with randomly and independently chosen spreading sequences accurately models the situation where pseudonoise sequences span many symbol periods. Furthermore, its analysis provides a comparison baseline for CDMA channels with deterministic signature waveforms spanning one symbol period. We analyze the spectral efficiency (total capacity per chip) as a function of the number of users, spreading gain, and signal-to-noise ratio, and we quantify the loss in efficiency relative to an optimally chosen set of signature sequences and relative to multiaccess with no spreading. White Gaussian background noise and equal-power synchronous users are assumed. The following receivers are analyzed: (a) optimal joint processing, (b) single-user matched filtering, (c) decorrelation, and (d) MMSE linear processing.

1,015 citations


Journal ArticleDOI
TL;DR: In this paper, a combination of white noise and flicker noise appears to be the best model for the noise characteristics of all three position components of a GPS coordinate time series, with the white noise amplitudes smallest in the north component and largest in the vertical component.
Abstract: We assess the noise characteristics in time series of daily position estimates for 23 globally distributed Global Positioning System (GPS) stations with 3 years of data, using spectral analysis and Maximum Likelihood Estimation. A combination of white noise and flicker noise appears to be the best model for the noise characteristics of all three position components. Both white and flicker noise amplitudes are smallest in the north component and largest in the vertical component. The white noise part of the vertical component is higher for tropical stations (+23 o latitude) compared to midlatitude stations. Velocity error in a GPS coordinate time series may be underestimated by factors of 5-11 if a pure white noise model is assumed.

709 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that 1/f noise can be better than white noise for enhancing the response of a neuron to a weak signal, under certain circumstances, and the biological implications of 1 /f noise were discussed.
Abstract: Noise can assist neurons in the detection of weak signals via a mechanism known as stochastic resonance (SR). We demonstrate experimentally that SR-type effects can be obtained in rat sensory neurons with white noise, 1/f noise, or 1/f{sup 2} noise. For low-frequency input noise, we show that the optimal noise intensity is the lowest and the output signal-to-noise ratio the highest for conventional white noise. We also show that under certain circumstances, 1/f noise can be better than white noise for enhancing the response of a neuron to a weak signal. We present a theory to account for these results and discuss the biological implications of 1/f noise. {copyright} {ital 1999} {ital The American Physical Society}

260 citations


Journal ArticleDOI
TL;DR: In this paper, an almost sure convergent expansion of fractional Brownian motion in wavelets is presented, which decorrelates the high frequencies of the high frequency corrections of the wavelet expansion.
Abstract: We provide an almost sure convergent expansion of fractional Brownian motion in wavelets which decorrelates the high frequencies. Our approach generalizes Levy's midpoint displacement technique which is used to generate Brownian motion. The low-frequency terms in the expansion involve an independent fractional Brownian motion evaluated at discrete times or, alternatively, partial sums of a stationary fractional ARIMA time series. The wavelets fill in the gaps and provide the necessary high frequency corrections. We also obtain a way of constructing an arbitrary number of non-Gaussian continuous time processes whose second order properties are the same as those of fractional Brownian motion.

175 citations


Journal ArticleDOI
TL;DR: In this paper, the authors prove the existence and uniqueness of a real-valued process solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable.
Abstract: We prove the existence and uniqueness, for any time, of a real-valued process solving a nonlinear stochastic wave equation driven by a Gaussian noise white in time and correlated in the two-dimensional space variable. We prove that the solution is regular in the sense of the Malliavin calculus. We also give a decay condition on the covariance function of the noise under which the solution has Holder continuous trajectories and show that, under an additional ellipticity assumption, the law of the solution at any strictly positive time has a smooth density.

167 citations


Proceedings ArticleDOI
26 Sep 1999
TL;DR: Algorithms for filtering white gaussian noise and 50 Hz power line noise from ECG signals are analyzed and good filtering results are reported: noise reduction with only minor change of the ECG waveforms as confirmed by the high correlation values between the processed signal and the original one.
Abstract: We analyze algorithms for filtering white gaussian noise and 50 Hz power line noise from ECG signals. We used several wavelets to study their effect and efficiency in the filtering process. To deal with these different kinds of noises we used two distinct soft-thresholding techniques: the Donoho's statistical threshold estimator and a method developed by us. This last method exploits one of the wavelet processing main features: time-frequency relation. The de-noising methods led to good filtering results: noise reduction with only minor change of the ECG waveforms as confirmed by the high correlation values between the processed signal and the original one. These good results are due to a wavelet advantage over classical filtering-time-frequency relation-enabling the possibility of filtering noise in the same frequency band of the ECG signal with minimal interference.

136 citations


Journal ArticleDOI
TL;DR: Asymptotic normality for a class of subspace algorithms, which estimate the state in a first step, is derived and a consistency result for the system matrix estimates is given.

127 citations


Journal ArticleDOI
TL;DR: Predictions, based on explicit formulae and on simulations, indicate that for very short projection times relative to T, brown and pink noise models are usually optimistic relative to equivalent white noise model, and for projection timescales equal to and substantially greater than T, an equivalent brown or pink noise model usually predicts a greater extinction risk, unless CV is very large.

124 citations


Journal ArticleDOI
TL;DR: An adaptive method for suppressing wideband interferences in spread-spectrum (SS) communications based on the generalized Wigner-Hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise is proposed.
Abstract: The paper proposes an adaptive method for suppressing wideband interferences in spread-spectrum (SS) communications. The proposed method is based on the time-frequency representation of the received signal from which the parameters of an adaptive time-varying interference excision filter are estimated. The approach is based on the generalized Wigner-Hough transform as an effective way to estimate the instantaneous frequency of parametric signals embedded in noise. The performance of the proposed approach is evaluated in the presence of linear and sinusoidal FM interferences plus white Gaussian noise in terms of the SNR improvement factor and bit error rate (BER).

113 citations


Journal ArticleDOI
TL;DR: It is shown that for a given PWVD order, the estimator performance can be improved by a proper choice of the kernel coefficients in the PWVD by evaluating the statistical performance of this estimator in the case of additive white Gaussian noise.
Abstract: The peak of the polynomial Wigner-Ville distribution (PWVD) has been previously proposed as an estimator of the instantaneous frequency (IF) for a monocomponent polynomial frequency modulated (FM) signal. In this paper, we evaluate the statistical performance of this estimator in the case of additive white Gaussian noise and provide an analytical expression for the variance. We show that for a given PWVD order, the estimator performance can be improved by a proper choice of the kernel coefficients in the PWVD. A performance comparison between the PWVD based IF estimator and another previously proposed one based on the high-order ambiguity function (HAF) is also provided, Simulation results show that for a signal-to-noise ratio larger than 3 dB, the proposed sixth-order PWVD outperforms the HAF in estimating the IF of a third- or fourth-order polynomial phase signal, evaluated at the central point of the observation interval.

112 citations


Book ChapterDOI
12 Aug 1999
TL;DR: The scheme of a device that should have a simple and reliable implementation and that, under simply verifiable conditions, should generate a true random binary sequence is defined and it is shown that the system is robust to changes in the circuit parameters.
Abstract: The scheme of a device that should have a simple and reliable implementation and that, under simply verifiable conditions, should generate a true random binary sequence is defined. Some tricks are used to suppress bias and correlation so that the desired statistical properties are obtained without using any pseudorandom transformation. The proposed scheme is well represented by an analytic model that describes the system behaviour both under normal conditions and when different failures occur. Within the model, it is shown that the system is robust to changes in the circuit parameters. Furthermore, a test procedure can be defined to verify the correct operation of the generator without performing any statistical analysis of its output.

Journal ArticleDOI
TL;DR: In this paper, a stochastic Korteweg-de-vries equation on the real line was considered and the authors used function spaces similar to those introduced by Bourgain to prove well posedness results.

Journal ArticleDOI
TL;DR: In this article, a general, computationally efficient method for chaotic signal estimation based on the connection between the symbolic sequence and the initial condition of a chaotic system is presented, which attains the Cramer-Rao lower bound at high signal-to-noise ratios.
Abstract: This article presents a general, computationally efficient method for chaotic signal estimation based on the connection between the symbolic sequence and the initial condition of a chaotic system. The performance of the method in white Gaussian noise is evaluated. The new method is asymptotically unbiased and attains the Cramer-Rao lower bound at high signal-to-noise ratios.

Journal ArticleDOI
TL;DR: In this article, a large deviation principle for a class of semilinear stochastic partial differential equations driven by space-time white noise was proved for the Burgers equation and the parabolic SPDEs.

Journal ArticleDOI
TL;DR: A statistical test is derived and shown to be the uniformly most powerful (UMP) test invariant to a group of transformations which are natural to the hypothesis testing problem.
Abstract: A statistical method for detecting activated pixels in functional MRI (fMRI) data is presented. In this method, the fMRI time series measured at each pixel is modeled as the sum of a response signal which arises due to the experimentally controlled activation-baseline pattern, a nuisance component representing effects of no interest, and Gaussian white noise. For periodic activation-baseline patterns, the response signal is modeled by a truncated Fourier series with a known fundamental frequency but unknown Fourier coefficients. The nuisance subspace is assumed to be unknown. A maximum likelihood estimate is derived for the component of the nuisance subspace which is orthogonal to the response signal subspace. An estimate for the order of the nuisance subspace is obtained from an information theoretic criterion. A statistical test is derived and shown to be the uniformly most powerful (UMP) test invariant to a group of transformations which are natural to the hypothesis testing problem. The maximal invariant statistic used in this test has an F distribution. The theoretical F distribution under the null hypothesis strongly concurred with the experimental frequency distribution obtained by performing null experiments in which the subjects did not perform any activation task. Applications of the theory to motor activation and visual stimulation fMRI studies are presented.

Journal ArticleDOI
TL;DR: In this article, a new procedure was proposed to automatically determine the cutoff frequency for low-pass filtering of biomechanical data, based on the properties of the autocorrelation function of white noise.
Abstract: This article presents and evaluates a new procedure that automatically determines the cutoff frequency for the low-pass filtering of biomechanical data. The cutoff frequency was estimated by exploiting the properties of the autocorrelation function of white noise. The new procedure systematically varies the cutoff frequency of a Butterworth filter until the signal representing the difference between the filtered and unfiltered data is the best approximation to white noise as assessed using the autocorrelation function. The procedure was evaluated using signals generated from mathematical functions. Noise was added to these signals so mat they approximated signals arising from me analysis of human movement. The optimal cutoff frequency was computed by finding the cutoff frequency that gave me smallest difference between the estimated and true signal values. The new procedure produced similar cutoff frequencies and root mean square differences to me optimal values, for me zeroth, first and second derivative...

Journal ArticleDOI
TL;DR: In this article, the authors compared the performance of the Bartlett's procedure and the Welch method for single real tone detection and frequency estimation in the presence of white Gaussian noise, and showed that the standard periodogram gives the optimum detection performance for a pure tone while the Welch algorithm is the best detector when there is phase instability in the sinusoid.
Abstract: With the advent of the fast Fourier transform (FFT) algorithm, the periodogram and its variants such as the Bartlett's procedure and Welch method, have become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these methods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the estimation errors become several orders of magnitude greater than the Cramer-Rao lower bound (CRLB), is also investigated. It is shown that the standard periodogram gives the optimum detection performance for a pure tone while the Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum likelihood estimator of frequency, it generally provides the minimum mean square frequency estimation errors.

Journal ArticleDOI
K. Nishiyama1
TL;DR: Simulations demonstrate that the HSE is more robust to the nature of observation noise {v/sub k/} than the Kalman sinusoidal estimator (KSE), which is an improved version of the nonlinear filter previously proposed by the author.
Abstract: A novel robust estimator is proposed for extracting a single complex sinusoid and its parameter (frequency) from measurements corrupted by white noise. This estimator is called an H/sub /spl infin// sinusoidal estimator (HSE), which is derived by applying an H/sub /spl infin// filter to a noisy sinusoidal model with the state-space representation. Simulations demonstrate that the HSE is more robust to the nature of observation noise {v/sub k/} than the Kalman sinusoidal estimator (KSE), which is an improved version of the nonlinear filter previously proposed by the author.

Journal ArticleDOI
TL;DR: In this paper, the authors considered the stochastic evolution equation with continuous one-sided linearly bounded "drift" F that is of at most polynomial growth and proved existence of a solution and uniqueness in the case when dW is space-time white and the spatial domain is allowed to be unbounded.
Abstract: We consider the stochastic evolution equation with continuous one-sided linearly bounded “drift” F that is of at most polynomial growth. The “diffusion” is globally Lipschitz continuous, while the driving term dW is either a space-time Gaussian white noise or correlated in space and white in time. The spatial domain is allowed to be unbounded. A covers a general class of operators including uniformly elliptic differential operators. We prove existence of a solution and uniqueness in the case when dW is space-time white and the spatial domain is bounded

Proceedings ArticleDOI
B. Muquet1, M. de Courville
15 Mar 1999
TL;DR: Two new blind channel identification methods suited to multicarrier system (OFDM) exploiting the redundancy introduced by the adjunction of a cyclic prefix at the emitter and relying on the evaluation of the received signal autocorrelation matrix are presented.
Abstract: Two new blind channel identification methods suited to multicarrier system (OFDM) exploiting the redundancy introduced by the adjunction of a cyclic prefix at the emitter and relying on the evaluation of the received signal autocorrelation matrix are presented. The proposed algorithms are able to identify any channel without any constraint on their zeroes location (including non-minimum phase channels) and are robust to the addition of white noise. Moreover a further enhancement of the estimation accuracy can easily be achieved by taking advantage of already present training symbols in current systems operating in a semi-blind context. Furthermore one of the two identification strategies has a very low arithmetical complexity which makes it particularly attractive in practice. Notice that these methods are not restricted to classical DFT-type modulators and still apply with any perfect reconstruction modulator.

Journal ArticleDOI
TL;DR: In this paper, the authors examined the importance of coloured noise for extinction risk using true 1/f noise and found that pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate.
Abstract: Analysis of long time series suggests that environmental fluctuations may be accurately represented by 1/f noise (pink noise), where temporal correlation is found at several scales, and the range of fluctuations increases over time. Previous studies on the effects of coloured noise on population dynamics used first or second order autoregressive noise. I examined the importance of coloured noise for extinction risk using true 1/f noise. I also considered the problem of estimating extinction risk with a limited sample of environmental variation. Pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate. However, pink noise environments decreased extinction risk in the Ricker model where environmental variation modified the carrying capacity. Underestimation of environmental variance almost always yielded underestimation of extinction risk. For either population viability analysis or management, we should carefully consider the long-term behaviour of the environment as well as how we include environmental noise in population models.

Journal ArticleDOI
TL;DR: In this paper, a numerical method is given for the solution of the probability density function of the response process of memoryless one-and two-state dynamical systems having polynomial restoring forces and which are subjected to a combination of Gaussian and Poisson white noises.

Journal ArticleDOI
TL;DR: In this article, a new least-squares method is developed which is based on a simple technique of estimating the observation noise variance by increasing the degree of the underlying AR model by one.
Abstract: The problem of estimating the unknown parameters of an autoregressive (AR) signal observed in white noise, including the signal power and the noise variance, is studied. A new type of least-squares method is developed which is based on a simple technique of estimating the observation noise variance by increasing the degree of the underlying AR model by one. The main feature of the presented method is that the consistent estimates of AR parameters can be directly achieved, with no need to prefilter noisy data or to make any parameter transformation.

Journal ArticleDOI
TL;DR: In this article, the authors prove exponential asymptotic stability for discrete-time filters for signals arising as solutions of d-dimensional stochastic difference equations, where the observation process is the signal corrupted by an additive white noise of sufficiently small variance.

Journal ArticleDOI
TL;DR: A new simple method using singular value decomposition (SVD) is presented for reducing noise from a sampled signal where the deterministic signal is from a low-dimensional chaotic dynamical system.

Journal ArticleDOI
TL;DR: Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed and are shown to be equivalent to the nonlinear least squares estimators.
Abstract: The problem of estimating the phase parameters of a phase-modulated signal in the presence of colored multiplicative noise (random amplitude modulation) and additive white noise (both Gaussian) is addressed. Closed-form expressions for the exact and large-sample Cramer-Rao Bounds (CRBs) are derived. It is shown that the CRB is significantly affected by the color of the modulating process when the signal-to-noise ratio (SNR) or the intrinsic SNR is small. Maximum likelihood type estimators that ignore the noise color and optimize a criterion with respect to only the phase parameters are proposed. These estimators are shown to be equivalent to the nonlinear least squares estimators, which consist of matching the squared observations with a constant amplitude phase-modulated signal when the mean of the multiplicative noise is forced to zero. Closed-form expressions are derived for the efficiency of these estimators and are verified via simulations.

Journal ArticleDOI
TL;DR: The original application of wavelets in statistics was to the estimation of a curve given observations of the curve plus white noise at 2J regularly spaced points as discussed by the authors, and the rationale for the use of wave...
Abstract: The original application of wavelets in statistics was to the estimation of a curve given observations of the curve plus white noise at 2J regularly spaced points. The rationale for the use of wave...

Journal ArticleDOI
TL;DR: This letter presents an alternative solution that does not require the explicit estimation of the noise and the driving process variances and deals with a new formulation of the approach proposed within a control literature framework by Mehra (1970).
Abstract: A great deal of attention has been paid to speech enhancement using a single microphone system. The various approaches, based on the Kalman filter, operate in two steps: (1) the noise variances and the parameters of the speech model are estimated, and (2) the speech signal is retrieved using standard Kalman filtering. This letter presents an alternative solution that does not require the explicit estimation of the noise and the driving process variances. This deals with a new formulation of the approach proposed within a control literature framework by Mehra (1970).

Book ChapterDOI
TL;DR: In this article, it was shown that, from the view of random dynamical systems, the deterministic Hopf bifurcation is being destroyed by parametric noise in the following sense: the system has a unique invariant measure which is exponentially stable in the sense that its top Lyapunov exponent is negative.
Abstract: We perform mainly a numerical study of the bifurcation behavior of the Brusselator under parametric white noise. It was shown before that parametric noise turns the deterministic Hopf bifurcation into a scenario in which the stationary density (unique solution of the Fokker- Planck equation) undergoes a delayed transition from a single-peaked, bellshaped to a crater-type form. We will make this more precise by showing that the stationary density gets a “dent” at the deterministic bifurcation point and develops a local minimum at a later parameter value. In contrast (but not in contradiction) to these findings we will show that, from the view point of random dynamical systems, the deterministic Hopf bifurcation is being “destroyed” by parametric noise in the following sense: For all values of the bifurcation parameter, the system has a unique invariant measure which is, moreover, exponentially stable in the sense that its top Lyapunov exponent is negative. The invariant measure is a random Dirac measure, and its support is the global random attractor of the system.

Journal ArticleDOI
TL;DR: In this article, the authors present a performance analysis of the feed-forward active noise control (ANC) system for ducts under the non-causality condition, showing that the bandwidth of the noise controllable by the ANC system decreases as the degree of non causality increases.
Abstract: Feedforward active noise control (ANC) systems function as adaptive system identification, thus able to control both broadband and narrowband noises. When the acoustic/electric delays in the noise cancelling subsystem exceed the acoustic delay of the primary path, the causality constraint will be violated. We present a performance analysis of the feedforward ANC system for ducts (one-dimensional acoustic field) under the noncausal condition. The bandwidth of the noise controllable by the ANC system decreases as the degree of noncausality increases. Noise with narrower bandwidth can be more effectively cancelled out by the ANC system with a given degree of noncausality. Analysis also shows that the convergence speed for the adaptive weight vector is independent of the degree of noncausality.