Showing papers on "White noise published in 2010"
01 Jan 2010
TL;DR: In this article, the authors present formulas relevant for time series analysis: 31.1. Predictions in Time Series, 31.2. Decomposition of (economic) Time Series and 31.3. Estimation of Correlation and Spectral Characteristics.
Abstract: Chapter 31 contains formulas relevant for time series analysis: 31.1. Predictions in Time Series, 31.2. Decomposition of (Economic) Time Series, 31.3. Estimation of Correlation and Spectral Characteristics, 31.4. Linear Time Series, 31.5 Nonlinear and Financial Time Series, 31.6 Multivariate Time Series, 31.7. Kalman Filter.
453 citations
TL;DR: A general mathematical and experimental methodology to compare and classify classical image denoising algorithms and a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image are defined.
Abstract: The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics. In spite of the sophistication of the recently proposed methods, most algorithms have not yet attained a desirable level of applicability. All show an outstanding performance when the image model corresponds to the algorithm assumptions but fail in general and create artifacts or remove fine structures in images. The main focus of this paper is, first, to define a general mathematical and experimental methodology to compare and classify classical image denoising algorithms and, second, to propose a nonlocal means (NL-means) algorithm addressing the preservation of structure in a digital image. The mathematical analysis is based on the analysis of the “method noise,” defined as the difference between a digital image and its denoised version. The NL-means algorithm is proven to be asymptotically optimal under a generic statistical image model. The denoising performance of all considered methods is compared in four ways; mathematical: asymptotic order of magnitude of the method noise under regularity assumptions; perceptual-mathematical: the algorithms artifacts and their explanation as a violation of the image model; quantitative experimental: by tables of $L^2$ distances of the denoised version to the original image. The fourth and perhaps most powerful evaluation method is, however, the visualization of the method noise on natural images. The more this method noise looks like a real white noise, the better the method.
445 citations
TL;DR: By making different assumptions on the availability of the white noise power value at the CR receiver, two algorithms are derived that are shown to outperform the standard energy detector.
Abstract: In this letter, we propose multi-antenna based spectrum sensing methods for cognitive radios (CRs) using the generalized likelihood ratio test (GLRT) paradigm. The proposed methods utilize the eigenvalues of the sample covariance matrix of the received signal vector from multiple antennas, taking advantage of the fact that in practice, the primary user signals to be detected will either occupy a subspace of dimension strictly smaller than the dimension of the observation space, or have a non-white spatial spectrum. These methods do not require prior knowledge of the primary user signals, or the channels from the primary users to the CR. By making different assumptions on the availability of the white noise power value at the CR receiver, we derive two algorithms that are shown to outperform the standard energy detector.
401 citations
Journal Article•
TL;DR: An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block and is shown to be convergent in the absence of noise and convergence with probability one in the presence of white noise.
Abstract: An optimal two-stage identification algorithm is presented for Hammerstein–Wiener systems where two static nonlinear elements surround a linear block. The proposed algorithm consists of two steps: The first one is the recursive least squares and the second one is the singular value decomposition of two matrices whose dimensions are fixed and do not increase as the number of the data point increases. Moreover, the algorithm is shown to be convergent in the absence of noise and convergent with probability one in the presence of white noise.
398 citations
TL;DR: An improved practical version of this method is provided by combining it with a reduced version of the dynamic programming algorithm and it is proved that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate.
Abstract: We propose a new approach for dealing with the estimation of the location of change-points in one-dimensional piecewise constant signals observed in white noise. Our approach consists in reframing this task in a variable selection context. We use a penalized least-square criterion with a l1-type penalty for this purpose. We explain how to implement this method in practice by using the LARS / LASSO algorithm. We then prove that, in an appropriate asymptotic framework, this method provides consistent estimators of the change points with an almost optimal rate. We finally provide an improved practical version of this method by combining it with a reduced version of the dynamic programming algorithm and we successfully compare it with classical methods.
329 citations
TL;DR: In this paper, a nonlinear piezomagneto-elastic energy harvester driven by stationary Gaussian white noise is considered and the simulated response of this validated model to random base excitation is considered.
Abstract: This letter considers a nonlinear piezomagnetoelastic energy harvester driven by stationary Gaussian white noise. The increase in the energy generated by this device has been demonstrated for harmonic excitation with slowly varying frequency in simulation and validated by experiment. This paper considers the simulated response of this validated model to random base excitation and shows that the system exhibits a stochastic resonance. If the variance of the excitation were known then the device may be optimized to maximize the power harvested, even under random excitation.
310 citations
TL;DR: This work provides insight on the advantages and drawbacks of l1 relaxation techniques such as BPDN and the Dantzig selector, as opposed to greedy approaches such as OMP and thresholding and provides theoretical performance guarantees for three sparse estimation algorithms.
Abstract: We consider the problem of estimating a deterministic sparse vector x0 from underdetermined measurements A x0 + w, where w represents white Gaussian noise and A is a given deterministic dictionary. We provide theoretical performance guarantees for three sparse estimation algorithms: basis pursuit denoising (BPDN), orthogonal matching pursuit (OMP), and thresholding. The performance of these techniques is quantified as the l2 distance between the estimate and the true value of x0. We demonstrate that, with high probability, the analyzed algorithms come close to the behavior of the oracle estimator, which knows the locations of the nonzero elements in x0. Our results are non-asymptotic and are based only on the coherence of A, so that they are applicable to arbitrary dictionaries. This provides insight on the advantages and drawbacks of l1 relaxation techniques such as BPDN and the Dantzig selector, as opposed to greedy approaches such as OMP and thresholding.
262 citations
TL;DR: In this article, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes.
Abstract: Fractal time series substantially differs from conventional one in its statistic properties. For instance, it may have a heavy-tailed probability distribution function (PDF), a slowly decayed autocorrelation function (ACF), and a power spectrum function (PSD) of type. It may have the statistical dependence, either long-range dependence (LRD) or short-range dependence (SRD), and global or local self-similarity. This article will give a tutorial review about those concepts. Note that a conventional time series can be regarded as the solution to a differential equation of integer order with the excitation of white noise in mathematics. In engineering, such as mechanical engineering or electronics engineering, engineers may usually consider it as the output or response of a differential system or filter of integer order under the excitation of white noise. In this paper, a fractal time series is taken as the solution to a differential equation of fractional order or a response of a fractional system or a fractional filter driven with a white noise in the domain of stochastic processes.
214 citations
TL;DR: The achievable signal-to-noise ratio (SNR) due to both additive white noise and multiplicative noise is discussed, and the corresponding sensitivity limit for trace gas detection is discussed.
Abstract: Coherent dual comb spectroscopy can provide high-resolution, high-accuracy measurements of a sample response in both magnitude and phase. We discuss the achievable signal-to-noise ratio (SNR) due to both additive white noise and multiplicative noise, and the corresponding sensitivity limit for trace gas detection. We show that sequential acquisition of the overall spectrum through a tunable filter, or parallel acquisition of the overall spectrum through a detector array, can significantly improve the SNR under some circumstances. We identify a useful figure of merit as the quality factor, equal to the product of the SNR, normalized by the square root of the acquisition time, and the number of resolved frequency elements. For a single detector and fiber-laser based system, this quality factor is 106 – 107 Hz1/2.
212 citations
TL;DR: In this paper, the performance of different minimization functionals such as the least squares norm 2, the least absolute values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to two offshore and onshore Valhallmodelandonshore overthrust model synthetic data sets were investigated in 2D elastic frequency-domain fullwaveform inversion FWI.
Abstract: Elastic full-waveform inversion is an ill-posed data-fitting procedure that is sensitive to noise, inaccuracies of the starting model,definitionofmultiparameterclasses,andinaccuratemodeling of wavefield amplitudes. We have investigated the performance of different minimization functionals as the least-squares norm 2, the least-absolute-values norm 1, and combinations of both the Huber and so-called hybrid criteria with reference to twonoisyoffshoreValhallmodelandonshoreoverthrustmodel synthetic data sets. The four minimization functionals were implemented in 2D elastic frequency-domain full-waveform inversion FWI, where efficient multiscale strategies were designed by successive inversions of a few increasing frequencies. For the offshore and onshore case studies, the 1-norm provided the most reliable models for P- and S-wave velocities VP and VS, even when strongly decimated data sets that correspond to fewfrequencieswereusedintheinversionandwhenoutlierspolluted the data. The 2-norm can provide reliable results in the presence of uniform white noise for VP and VS if the data redundancyisincreasedbyrefiningthefrequencysamplingintervalin the inversion at the expense of computational efficiency. The 1-norm and the Huber and hybrid criteria, unlike the 2-norm, allowforsuccessfulimagingoftheVSmodelfromnoisydataina soft-seabed environment, where the P-to-S-waves have a small footprint in the data. However, the Huber and hybrid criteria are sensitive to a threshold criterion that controls the transition between the criteria and that requires tedious trial-and-error investigations for reliable estimation. The 1-norm provides a robust alternativetothe2-normforinvertingdecimateddatasetsinthe frameworkofefficientfrequency-domainFWI.
210 citations
Journal Article•
TL;DR: In this paper, a blind approach to the sampled Hammerstein-Wiener model identification is proposed, where no a priori structural knowledge about the input nonlinearity is assumed and no white noise assumption is imposed on the input.
Abstract: In this paper, we propose a blind approach to the sampled Hammerstein-Wiener model identification. By using the blind approach, it is shown that all internal variables can be recovered solely based on the output measurements. Then, 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, a frequency pattern and a competent criterion are introduced for short-circuit-fault recognition in permanent-magnet synchronous motors (PMSMs), where the frequency pattern is extracted from the monitored stator current analytically and the amplitude of sideband components at these frequencies is introduced as a proper criterion to determine the number of shortcircuited turns.
Abstract: In this paper, a novel frequency pattern and competent criterion are introduced for short-circuit-fault recognition in permanent-magnet synchronous motors (PMSMs). The frequency pattern is extracted from the monitored stator current analytically and the amplitude of sideband components at these frequencies is introduced as a proper criterion to determine the number of short-circuited turns. Impacts of the load variation on the proposed criterion are investigated in the faulty PMSM. In order to demonstrate the aptitude of the proposed criterion for precise short-circuit fault detection, the relation between the nominated criterion and the number of short-circuited turns is specified by the mutual information index. Therefore, a white Gaussian noise is added to the simulated stator current and robustness of the criterion is analyzed with respect to the noise variance. The occurrence and the number of short-circuited turns are predicted using support-vector machine as a classifier. The classification results indicate that the introduced criterion can detect the short-circuit fault incisively. Simulation results are verified by the experimental results.
TL;DR: It is found that under the influence of noise, Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution.
Abstract: We investigate the influence of additive Gaussian white noise on two different bistable self-sustained oscillators: Duffing-Van der Pol oscillator with hard excitation and a model of a synthetic genetic oscillator. In the deterministic case, both oscillators are characterized with a coexistence of a stable limit cycle and a stable equilibrium state. We find that under the influence of noise, their dynamics can be well characterized through the concept of stochastic bifurcation, consisting in a qualitative change of the stationary amplitude distribution. For the Duffing-Van der Pol oscillator analytical results, obtained for a quasiharmonic approach, are compared with the result of direct computer simulations. In particular, we show that the dynamics is different for isochronous and anisochronous systems. Moreover, we find that the increase of noise intensity in the isochronous regime leads to a narrowing of the spectral line. This effect is similar to coherence resonance. However, in the case of anisochronous systems, this effect breaks down and a new phenomenon, anisochronous-based stochastic bifurcation occurs.
TL;DR: A stochastic source seeking control law is designed which employs excitation based on filtered white noise, rather than sinusoidal perturbations used in the existing work, and local exponential convergence is proved, both almost surely and in probability, to a small neighborhood near the source.
TL;DR: A new approach for the detection and classification of single and combined power quality (PQ) disturbances is proposed using fuzzy logic and a particle swarm optimization (PSO) algorithm.
TL;DR: The formulas of computing the cross-covariances among local estimation errors are proposed and two Monte Carlo simulation examples for an infrared target tracking system and a Bernoulli-Gaussian white noise deconvolution system show their effectiveness.
TL;DR: The main feature of the proposed method is that it uses the strength of glottal activity as against using the periodicity of the signal to distinguish voiced epochs from random instants detected in nonvoiced regions.
Abstract: In this paper, a new method for voiced/nonvoiced detection based on epoch extraction is proposed. Zero-frequency filtered speech signal is used to extract the instants of significant excitation (or epochs). The robustness of the method to extract epochs in the voiced regions, even with small amount of additive white noise, is used to distinguish voiced epochs from random instants detected in nonvoiced regions. The main feature of the proposed method is that it uses the strength of glottal activity as against using the periodicity of the signal. Performance of the proposed algorithm is studied on TIMIT and CMU ARCTIC databases, for two different noise types, white and vehicle noise from the NOISEX database, at different signal-to-noise ratios (SNRs). The proposed method performs similar or better than the popular normalized crosscorrelation based voiced/nonvoiced detection used in the open source utility wavesurfer, especially at lower SNRs.
01 Jan 2010
TL;DR: The characteristics of Gaussian white noise are studied by using the empirical mode decomposition (EMD) method and these methods are applied to well-studied geophysical datasets to demonstrate the method’s validity and effectiveness.
Abstract: One of the preliminary tasks when analyzing a dataset is to determine whether it or its components contain useful information. The task is essentially a binary hypothesis testing problem in which a null hypothesis of pure noise is often preproposed. To test against the null hypothesis, the characteristics of noise need to be understood first, and often, these characteristics pertain to the analysis method used. In this paper, the characteristics of Gaussian white noise are studied by using the empirical mode decomposition (EMD) method. Statistical testing methods for Gaussian white noise for the intrinsic mode functions (IMFs) are designed based on the characteristics of Gaussian white noise by using EMD. These methods are applied to well-studied geophysical datasets to demonstrate the method’s validity and effectiveness.
TL;DR: An engineering approach known as systems identification is applied to quantify the in vivo interactions in the p53–mdm2 feedback loop on the basis of accurate measurements of its power spectrum, finding characteristic spectra with distinct low-frequency components that are well-described by a third-order linear model with white noise.
Abstract: A key circuit in the response of cells to damage is the p53–mdm2 feedback loop. This circuit shows sustained, noisy oscillations in individual human cells following DNA breaks. Here, we apply an engineering approach known as systems identification to quantify the in vivo interactions in the circuit on the basis of accurate measurements of its power spectrum. We obtained oscillation time courses of p53 and Mdm2 protein levels from several hundred cells and analyzed their Fourier spectra. We find characteristic spectra with distinct low-frequency components that are well-described by a third-order linear model with white noise. The model identifies the sign and strength of the known interactions, including a negative feedback loop between p53 and its upstream regulator. It also implies that noise can trigger and maintain the oscillations. The model also captures the power spectra of p53 dynamics without DNA damage. Parameters such as noise amplitudes and protein lifetimes are estimated. This approach employs natural biological noise as a diagnostic that stimulates the system at many frequencies at once. It seems to be a useful way to find the in vivo design of circuits and may be applied to other systems by monitoring their power spectrum in individual cells.
TL;DR: The weighted multipoint interpolated discrete Fourier transform method is considered, and its effect on both the spectral interference due to the image component and the additive wideband noise is taken into account.
Abstract: This paper focuses on the frequency-domain estimation of the normalized frequency of a sine wave corrupted by a stationary white noise. The weighted multipoint interpolated discrete Fourier transform method is considered, and its effect on both the spectral interference due to the image component and the additive wideband noise is taken into account. In particular, the expression of the combined standard uncertainty of the estimator is derived in the case when the H-term maximum sidelobe decay window (H ≥ 2) is used, and the number of interpolation points is 2J + 1 (J ≥ 1). Based on this expression, the number of interpolation points that minimize the estimator-combined uncertainty can be determined. The derived results are validated by means of computer simulations and applied to experimental data.
TL;DR: In this article, a modified version of the Universal Phase-Space-Thresholding technique was used to detect spikes and replace them with the last valid data points, which can accurately recover the power spectra up to the frequency corresponding to the half the mean sampling rate of the valid points.
Abstract: Spectral analysis of velocity signals recorded by acoustic-Doppler velocimetry (ADV) and contaminated with intermittent spikes remains a challenging task. In this paper, we propose a new method for reconstructing contaminated time series, which integrates two previously developed techniques for detecting and replacing spurious spikes. The spikes are first detected using a modified version of the Universal Phase-Space-Thresholding technique and subsequently replaced by the last valid data points. The accuracy of the new approach is evaluated by applying it to identify and remove spikes and reconstruct the spectra of two clean data sets which are artificially contaminated with random spikes: (a) high-quality hot-wire measurement; and (b) numerically simulated velocity time series with bi-modal probability density distribution. The technique is also applied to reconstruct the spectra obtained from intentionally contaminated ADV measurements and compare them with ADV spectra at the same point in the flow obtained using proper ADV settings. Special emphasis is placed on testing the ability of the technique to reproduce realistic power spectra in flows with rich coherent dynamics. The results show that the power spectra of the reconstructed time series contain a filtered white noise caused by the steps in the reconstruction technique using the last valid data point. We show that even for a severely contaminated time series, the proposed method can accurately recover the power spectra up to the frequency corresponding to the half the mean sampling rate of the valid data points.
TL;DR: A filtered-X LMS (FXLMS) based narrowband ANC system is analyzed, whose online secondary-path modeling is based on the use of an auxiliary white noise scaled by one-sample-delayed residual noise signal.
Abstract: Online secondary-path modeling of active noise control (ANC) systems may be effectively implemented by injecting an auxiliary white noise whose magnitude is scaled by a function of residual noise signal. In this paper, a filtered-X LMS (FXLMS) based narrowband ANC system is analyzed, whose online secondary-path modeling is based on the use of an auxiliary white noise scaled by one-sample-delayed residual noise signal. Difference equations governing the dynamics of the entire system and closed-form expressions for steady-state mean-square errors (MSE) as well as the residual noise power are derived and discussed in detail. Extensive simulations are conducted to confirm the validity of the analytical findings.
TL;DR: Experiments suggest that appropriate power thresholding can be a simple and good approximation to the sinusoidal modeling, for the purpose of selecting time-frequency points with high local SNR, with slight loss in performance.
Abstract: This paper proposes a two microphone-based source localization technique for multiple speech sources utilizing speech specific properties and novel clustering algorithms. Voiced speech is sparse in the frequency domain and can be represented by sinusoidal tracks via sinusoidal modeling which provides high local signal-to-noise ratio (SNR). By utilizing the inter-channel phase differences (IPDs) between the dual channels on the sinusoidal tracks, the source localization of the mixed multiple speech sources is turned into a clustering problem on the IPD versus frequency plot. The generalized mixture decomposition algorithm (GMDA) is used to cluster the groups of points corresponding to multiple sources and thus estimate the direction of arrival (DOA) of the sources. Experiments illustrate the proposed GMDA algorithm with the Laplacian noise model can estimate the number of sources accurately and exhibits smaller DOA estimation error than the baseline histogram based DOA estimation algorithm in various scenarios including reverberant and additive white noise environments. Experiments suggest that appropriate power thresholding can be a simple and good approximation to the sinusoidal modeling, for the purpose of selecting time-frequency points with high local SNR, with slight loss in performance.
TL;DR: The methodology can be used to estimate for any station how much the accuracy of the linear trend will improve when one tries to subtract the annual signal from the GPS time- series by using a physical model and it is demonstrated that for short time-series the trend error is more influenced by the fact that the noise properties also need to be estimated from the data.
TL;DR: In this paper, the spatial and time regularity of solutions to linear stochastic evolution equations perturbed by Levy white noise is investigated and sufficient conditions for spatial continuity are derived.
Abstract: The paper is concerned with spatial and time regularity of solutions to linear stochastic evolution equation perturbed by Levy white noise “obtained by subordination of a Gaussian white noise”. Sufficient conditions for spatial continuity are derived. It is also shown that solutions do not have in general cadlag modifications. General results are applied to equations with fractional Laplacian. Applications to Burgers stochastic equations are considered as well.
TL;DR: Simulation shows outstanding robustness of the proposed scheme against common attacks, especially additive white noise and JPEG compression.
Abstract: A robust image watermarking scheme in the ridgelet transform domain is proposed in this paper. Due to the use of the ridgelet domain, sparse representation of an image which deals with line singularities is obtained. In order to achieve more robustness and transparency, the watermark data is embedded in selected blocks of the host image by modifying the amplitude of the ridgelet coefficients which represent the most energetic direction. Since the probability distribution function of the ridgelet coefficients is not known, we propose a universally optimum decoder to perform the watermark extraction in a distribution-independent fashion. Decoder extracts the watermark data using the variance of the ridgelet coefficients of the most energetic direction in each block. Furthermore, since the decoder needs the noise variance to perform decoding, a robust noise estimation scheme is proposed. Moreover, the implementation of error correction codes on the proposed method is investigated. Analytical derivation of bit error probability is also carried out and experimental results prove its accuracy. Simulation also shows outstanding robustness of the proposed scheme against common attacks, especially additive white noise and JPEG compression.
TL;DR: An efficient likelihood ratio selection (LRS) procedure for identifying the segments is developed, and the asymptotic optimality of this method is presented in the sense that the LRS can separate the signal segments from the noise as long as the signals are in the identifiable regions.
Abstract: Motivated by DNA copy number variation (CNV) analysis based on high-density single nucleotide polymorphism (SNP) data, we consider the problem of detecting and identifying sparse short segments in a long one-dimensional sequence of data with additive Gaussian white noise, where the number, length, and location of the segments are unknown. We present a statistical characterization of the identifiable region of a segment where it is possible to reliably separate the segment from noise. An efficient likelihood ratio selection (LRS) procedure for identifying the segments is developed, and the asymptotic optimality of this method is presented in the sense that the LRS can separate the signal segments from the noise as long as the signal segments are in the identifiable regions. The proposed method is demonstrated with simulations and analysis of a real dataset on identification of copy number variants based on high-density SNP data. The results show that the LRS procedure can yield greater gain in power for de...
Patent•
09 Apr 2010TL;DR: In this article, a method of forming a beampattern in a beamformer of the type in which the beamformer receives input signals from a sensor array, decomposes the input signals into the spherical harmonics domain, applies weighting coefficients to the spherical harmonic and combines them to form an output signal, wherein the weighting coefficient are optimized for a given set of input parameters by convex optimization.
Abstract: A method of forming a beampattern in a beamformer of the type in which the beamformer receives input signals from a sensor array, decomposes the input signals into the spherical harmonics domain, applies weighting coefficients to the spherical harmonics and combines them to form an output signal, wherein the weighting coefficients are optimized for a given set of input parameters by convex optimization. Formulations are provided for forming second order cone programming constraints for multiple main lobe generation, uniform and non-uniform side lobe control, automatic null steering, robustness and white noise gain.
TL;DR: This work derives a necessary condition on the chosen precoding matrices for minimizing error probability of the OFDM system in the additive white Gaussian noise (AWGN) channel and proves that the precoding matrix with all the singular values equal to 1 is one of the optimal solutions.
Abstract: The precoding technique is an effective and flexible way for reducing the peak-to-average power ratio (PAPR) of orthogonal frequency division multiplexing (OFDM) signals. However, different precoding schemes will increase error probabilities of the system. With the knowledge of the channel information and the receiver filter, we derive a necessary condition on the chosen precoding matrices for minimizing error probability of the OFDM system in the additive white Gaussian noise (AWGN) channel. A systematic procedure in designing such an optimal precoding matrix is provided. With a proper selection, the optimal precoding matrix can meet the requirements of PAPR reduction and achieve the minimum error probability in white Gaussian noise. Our simulation results show that the chosen precoding matrix notably outperforms other general precoding matrices in both AWGN and multipath fading channels. We also proved that the precoding matrix with all the singular values equal to 1 is one of the optimal solutions.
TL;DR: In this article, a combined method of random decrement signature and neural networks is used to extract the free decay of the structure from its online response while the structure is in service.