Showing papers on "White noise published in 2016"

Comparative Performance Evaluation of Orthogonal-Signal-Generators-Based Single-Phase PLL Algorithms—A Survey

Abstract: The orthogonal-signal-generator-based phase-locked loops (OSG-PLLs) are among the most popular single-phase PLLs within the areas of power electronics and power systems, mainly because they are often easy to be implemented and offer a robust performance against the grid disturbances. The main aim of this paper is to present a survey of the comparative performance evaluation among the state-of-the-art OSG-PLLs (include Delay-PLL, Deri-PLL, Park-PLL, SOGI-PLL, DOEC-PLL, VTD-PLL, CCF-PLL, and TPFA-PLL) under different grid disturbances such as voltage sags, phase, and frequency jumps, and in the presence of dc offset, harmonic components, and white noise in their input. This analysis provides a useful insight about the advantages and disadvantages of these PLLs. The performance enhancement of Delay-PLL, Deri-PLL, and CCF-PLL by including a moving average filter into their structure is another goal of this paper.

Proper Image Subtraction—Optimal Transient Detection, Photometry, and Hypothesis Testing

Abstract: Transient detection and flux measurement via image subtraction stand at the base of time domain astronomy. Due to the varying seeing conditions, the image subtraction process is non-trivial, and existing solutions suffer from a variety of problems. Starting from basic statistical principles, we develop the optimal statistic for transient detection, flux measurement, and any image-difference hypothesis testing. We derive a closed-form statistic that: (1) is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise, (2) is numerically stable, (3) for accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts, (4) allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance, (5) has uncorrelated white noise, (6) is a sufficient statistic for any further statistical test on the difference image, and, in particular, allows us to distinguish particle hits and other image artifacts from real transients, (7) is symmetric to the exchange of the new and reference images, (8) is at least an order of magnitude faster to compute than some popular methods, and (9) is straightforward to implement. Furthermore, we present extensions of this method that make it resilient to registration errors, color-refraction errors, and any noise source that can be modeled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay & Ofek. We demonstrate this method on simulated data and real observations from the PTF data release 2. We provide an implementation of this algorithm in MATLAB and Python.

Transcranial Random Noise Stimulation of Visual Cortex: Stochastic Resonance Enhances Central Mechanisms of Perception.

Abstract: Random noise enhances the detectability of weak signals in nonlinear systems, a phenomenon known as stochastic resonance (SR). Though counterintuitive at first, SR has been demonstrated in a variety of naturally occurring processes, including human perception, where it has been shown that adding noise directly to weak visual, tactile, or auditory stimuli enhances detection performance. These results indicate that random noise can push subthreshold receptor potentials across the transfer threshold, causing action potentials in an otherwise silent afference. Despite the wealth of evidence demonstrating SR for noise added to a stimulus, relatively few studies have explored whether or not noise added directly to cortical networks enhances sensory detection. Here we administered transcranial random noise stimulation (tRNS; 100–640 Hz zero-mean Gaussian white noise) to the occipital region of human participants. For increasing tRNS intensities (ranging from 0 to 1.5 mA), the detection accuracy of a visual stimuli changed according to an inverted-U-shaped function, typical of the SR phenomenon. When the optimal level of noise was added to visual cortex, detection performance improved significantly relative to a zero noise condition (9.7 ± 4.6%) and to a similar extent as optimal noise added to the visual stimuli (11.2 ± 4.7%). Our results demonstrate that adding noise to cortical networks can improve human behavior and that tRNS is an appropriate tool to exploit this mechanism. SIGNIFICANCE STATEMENT Our findings suggest that neural processing at the network level exhibits nonlinear system properties that are sensitive to the stochastic resonance phenomenon and highlight the usefulness of tRNS as a tool to modulate human behavior. Since tRNS can be applied to all cortical areas, exploiting the SR phenomenon is not restricted to the perceptual domain, but can be used for other functions that depend on nonlinear neural dynamics (e.g., decision making, task switching, response inhibition, and many other processes). This will open new avenues for using tRNS to investigate brain function and enhance the behavior of healthy individuals or patients.

Proper image subtraction - optimal transient detection, photometry and hypothesis testing

Abstract: Transient detection and flux measurement via image subtraction stand at the base of time domain astronomy. Due to the varying seeing conditions, the image subtraction process is non-trivial, and existing solutions suffer from a variety of problems. Starting from basic statistical principles, we develop the optimal statistic for transient detection, flux measurement and any image-difference hypothesis testing. We derive a closed-form statistic that: (i) Is mathematically proven to be the optimal transient detection statistic in the limit of background-dominated noise; (ii) Is numerically stable; (iii) For accurately registered, adequately sampled images, does not leave subtraction or deconvolution artifacts; (iv) Allows automatic transient detection to the theoretical sensitivity limit by providing credible detection significance; (v) Has uncorrelated white noise; (vi) Is a sufficient statistic for any further statistical test on the difference image, and in particular, allows to distinguish particle hits and other image artifacts from real transients; (vii) Is symmetric to the exchange of the new and reference images; (viii) Is at least an order of magnitude faster to compute than some popular methods; and (ix) Is straightforward to implement. Furthermore, we present extensions of this method that make it resilient to registration errors, color-refraction errors, and any noise source that can be modelled. In addition, we show that the optimal way to prepare a reference image is the proper image coaddition presented in Zackay \& Ofek (2015b). We demonstrate this method on simulated data and real observations from the Palomar Transient Factory data release 2. We provide an implementation of this algorithm in MATLAB and Python.

Iterative Methods for Subspace and DOA Estimation in Nonuniform Noise

Abstract: Usually, direction-of-arrival (DOA) estimators are derived under the assumption of uniform white noise, whose covariance matrix is a scaled identity matrix. However, in practice, the noise can be nonuniform with an arbitrary unknown diagonal covariance matrix. In this situation, the performance of DOA estimators may be deteriorated considerably if the noise nonuniformity is ignored. To tackle this problem, iterative approaches to subspace estimation are developed and the corresponding subspace-based DOA estimators are addressed. In our proposed methods, the signal subspace and noise covariance matrix are first determined by maximizing the log-likelihood (LL) function or solving a least-squares (LS) minimization problem, both of which are accomplished in an iterative manner. Then, the DOAs are determined from the subspace estimate and/or noise covariance matrix estimate with the help of traditional DOA estimators. As the signal subspace and noise covariance matrix can be computed in closed-form in each iteration, the proposals are computationally attractive. Furthermore, the signal subspace is directly calculated without the requirement of the exact knowledge of the array manifold, enabling us to handle array uncertainties by incorporating conventional subspace-based calibration algorithms. Simulations and experimental results are included to demonstrate the superiority of the proposed approaches.

Modeling and Identification of Piezoelectric-Actuated Stages Cascading Hysteresis Nonlinearity With Linear Dynamics

Abstract: In this paper, we propose a new modeling and identification approach for piezoelectric-actuated stages cascading hysteresis nonlinearity with linear dynamics, which is described as a Hammerstein-like structure. In the proposed approach, the hysteresis and linear dynamics together with the delay time and higher order dynamic behaviors are obtained with three data-driven identification steps under designed input signals. In the first step, the step input signal is applied to estimate the delay time of the piezoelectric-actuated stages. In the second step, the autoregression with exogenous signal identification algorithm is adopted to identify the linear dynamics using a small-amplitude band-limited white noise input signal. In the third step, with the identified linear dynamics model, the parameters of the rate-independent Prandtl–Ishlinskii hysteresis model are identified by the particle swarm optimization algorithm using a simple low-frequency triangle input signal with different amplitudes. Finally, the experimental results on a piezoelectric-actuated stage show that both the hysteresis and dynamic behaviors of the piezoelectric-actuated stage are well predicted by the proposed modeling method. In addition, we provide the analysis of quantitative prediction errors of the identified model with comparison to experimental data, which clearly demonstrate the effectiveness of the proposed approach.

Signal Detection In Non Gaussian Noise

Abstract: A solution to get the problem off, have you found it? Really? What kind of solution do you resolve the problem? From what sources? Well, there are so many questions that we utter every day. No matter how you will get the solution, it will mean better. You can take the reference from some books. And the signal detection in non gaussian noise is one book that we really recommend you to read, to get more solutions in solving this problem.

Deep neural network-based automatic modulation classification technique

Abstract: Deep neural network (DNN) has recently received much attention due to its superior performance in classifying data with complex structure. In this paper, we investigate application of DNN technique to automatic classification of modulation classes for digitally modulated signals. First, we select twenty one statistical features which exhibit good separation in empirical distributions for all modulation formats considered (i.e., BPSK, QPSK, 8PSK, 16QAM, and 64QAM). These features are extracted from the received signal samples and used as the input to the fully connected DNN with three hidden layer. The training data containing 25,000 feature vectors is generated by the computer simulation under both additive Gaussian white noise (AWGN) and Rician fading channels. Our test results show that the proposed method brings dramatic performance improvement over the existing classifier especially for high Doppler fading channels.

Robust identification of OE model with constrained output using optimal input design

Abstract: This paper considers the robust algorithm for identification of OE (output error) model with constrained output in presence of non-Gaussian noises. In practical conditions, in measurements there are rare, inconsistent observations with the largest part of population of observations (outliers). The synthesis of robust algorithms is based on Huber׳s theory of robust statistics. Also, it is known fact that constraints play a very important role in many practical cases. If constraints are not taken into consideration, the control performance can corrupt and safety of a process may be at risk. The practical value of proposed robust algorithm for estimation of OE model parameters with constrained output variance is further increased by using an optimal input design. It is shown that the optimal input can be obtained by a minimum variance controller whose reference is a white noise sequence with known variance. A key problem is that the optimal input depends on system parameters to be identified. In order to be able to implement the proposed optimal input, the adaptive two-stage procedure for generating the input signal is proposed. Theoretical results are illustrated by simulations which show significant increasing of accuracy in parameter estimates of the OE model by using the robust identification procedure in relation to the linear identification algorithm for OE models. Also, it can be seen that the convergence rate of the robust algorithm is further increased by using the optimal input design, which increases the practical value of proposed robust procedure.

Environmental variability and mean-reverting processes

Abstract: Environmental variability is often incorporated in a mathematical model by modifying the parameters in the model. In the present investigation, two common methods to incorporate the effects of environmental variability in stochastic differential equation models are studied. The first approach hypothesizes that the parameter satisfies a mean-reverting stochastic process. The second approach hypothesizes that the parameter is a linear function of Gaussian white noise. The two approaches are discussed and compared analytically and computationally. Properties of several mean-reverting processes are compared with respect to nonnegativity and their asymptotic stationary behavior. The effects of different environmental variability assumptions on population size and persistence time for simple population models are studied and compared. Furthermore, environmental data are examined for a gold mining stock. It is concluded that mean-reverting processes possess several advantages over linear functions of white noise in modifying parameters for environmental variability.

Dissipativity analysis of memristive neural networks with time-varying delays and randomly occurring uncertainties

Abstract: Dissipativity theory is a very important concept in the field of control system. In this paper, we pay attention to the problem of dissipativity analysis of memristive neural networks with time-varying delay and randomly occurring uncertainties(ROUs). Under the framework of Filippov solution, differential inclusion theory, by employing a proper Lyapunov functional, and some inequality techniques, the dissipativity criteria are obtained in terms of LMIs. It should be noteworthy that the uncertainty terms as well as the ROUs are separately taken into consideration, in which the uncertainties are norm-bounded and the ROUs obey certain mutually uncorrelated Bernoulli-distributed white noise sequences. Finally, the effectiveness of the proposed method will be verified via numerical example. Copyright © 2015 John Wiley & Sons, Ltd.

Non-negative least-squares variance component estimation with application to GPS time series

Abstract: The problem of negative variance components is probable to occur in many geodetic applications. This problem can be avoided if non-negativity constraints on variance components (VCs) are introduced to the stochastic model. Based on the standard non-negative least-squares (NNLS) theory, this contribution presents the method of non-negative least-squares variance component estimation (NNLS-VCE). The method is easy to understand, simple to implement, and efficient in practice. The NNLS-VCE is then applied to the coordinate time series of the permanent GPS stations to simultaneously estimate the amplitudes of different noise components such as white noise, flicker noise, and random walk noise. If a noise model is unlikely to be present, its amplitude is automatically estimated to be zero. The results obtained from 350 GPS permanent stations indicate that the noise characteristics of the GPS time series are well described by combination of white noise and flicker noise. This indicates that all time series contain positive noise amplitudes for white and flicker noise. In addition, around two-thirds of the series consist of random walk noise, of which its average amplitude is the (small) value of 0.16, 0.13, and 0.45 $$\text{ mm/year }^{1/2}$$ for the north, east, and up components, respectively. Also, about half of the positive estimated amplitudes of random walk noise are statistically significant, indicating that one-third of the total time series have significant random walk noise.

Probability Density Functions of Stationary Surface EMG Signals in Noisy Environments

Abstract: The probability density function (pdf) of an electromyography (EMG) signal provides useful information for choosing an appropriate feature extraction technique. The pdf is influenced by many factors, including the level of contraction force, muscle type, and noise. In this paper, we investigated the pdfs of noisy EMG signals artificially contaminated with five different noise types: 1) Electrocardiography (ECG) interference; 2) many spurious background spikes; 3) white Gaussian noise; 4) motion artifact; and 5) power line interference at various levels of signal-to-noise ratio (SNR). In addition, we evaluated a set of statistical descriptors for identifying a noisy EMG signal from its pdf, specifically kurtosis, negentropy, L-kurtosis, and robust measures of kurtosis (KR1 and KR2). The results show that at low SNR (<5 dB), all noise types affect the statistical descriptors for the pdf of a noisy EMG signal. In addition, KR2 performs the best among these descriptors in identifying a noisy EMG signal from its pdf, because it is computed based on the quantiles of the data. As a result, it can avoid the effects of outliers resulting in the correct identification of pdf shape of noisy EMGs with all contamination types and all levels of SNR.

Stochastic averaging of energy harvesting systems

Abstract: A stochastic averaging method is proposed for nonlinear energy harvesters subjected to external white Gaussian noise and parametric excitations. The Fokker–Planck–Kolmogorov equation of the coupled electromechanical system of energy harvesting is a three variables nonlinear parabolic partial differential equation whose exact stationary solutions are generally hard to find. In order to overcome difficulties in solving higher dimensional nonlinear partial differential equations, a transformation scheme is applied to decouple the electromechanical equations. The averaged Ito equations are derived via the standard stochastic averaging method, then the FPK equations of the decoupled system are obtained. The exact stationary solution of the averaged FPK equation is used to determine the probability densities of the displacement, the velocity, the amplitude, the joint probability densities of the displacement and velocity, and the power of the stationary response. The effects of the system parameters on the output power are examined. The approximate analytical outcomes are qualitatively and quantitatively supported by the Monte Carlo simulations.

Optimal Filtering for Discrete-Time Linear Systems With Time-Correlated Multiplicative Measurement Noises

Abstract: In this note, the filtering problem for discrete-time linear systems with time-correlated multiplicative measurement noises is considered where the vector consisting of all the multiplicative measurement noises can be described by a linear system model with white noise. By introducing several new recursive terms, a novel algorithm for optimal filtering of the system under consideration is proposed in the sense of linear minimum mean-square error. The proposed algorithm is recursive and has time-independent complexity. Computer simulations are provided to illustrate the performance of the proposed algorithm.

Computing Transition Rates for the 1-D Stochastic Ginzburg–Landau–Allen–Cahn Equation for Finite-Amplitude Noise with a Rare Event Algorithm

Abstract: In this article we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen–Cahn equations for both the Freidlin–Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefactor given by the potential curvature grows exponentially with size. The main novelty of our work is that we also perform an analysis of reactive trajectories for large noises and large domains. In this case, we show that the position of the reactive front is essentially a random walk. This time, the mean duration grows linearly with the inverse temperature and quadratically with the size. Using a phenomenological description of the system, we are able to calculate the transition rate, although the dynamics is described by neither Freidlin–Wentzell or Eyring–Kramers type of results. Numerical results confirm our analysis.

Conditional and unconditional Gaussian quantum dynamics

Abstract: This article focuses on the general theory of open quantum systems in the Gaussian regime and explores a number of diverse ramifications and consequences of the theory. We shall first introduce the Gaussian framework in its full generality, including a classification of Gaussian (also known as "general-dyne") quantum measurements. In doing so, we will give a compact proof for the parametrisation of the most general Gaussian completely positive map, which we believe to be missing in the existing literature. We will then move on to consider the linear coupling with a white noise bath, and derive the diffusion equations that describe the evolution of Gaussian states under such circumstances. Starting from these equations, we outline a constructive method to derive general master equations that apply outside the Gaussian regime. Next, we include the general-dyne monitoring of the environmental degrees of freedom and recover the Riccati equation for the conditional evolution of Gaussian states. Our derivation relies exclusively on the standard quantum mechanical update of the system state, through the evaluation of Gaussian overlaps. The parametrisation of the conditional dynamics we obtain is novel and, at variance with existing alternatives, directly ties in to physical detection schemes. We conclude our study with two examples of conditional dynamics that can be dealt with conveniently through our formalism, demonstrating how monitoring can suppress the noise in optical parametric processes as well as stabilise systems subject to diffusive scattering.

Characterizations of variational source conditions, converse results, and maxisets of spectral regularization methods

Abstract: We describe a general strategy for the verification of variational source condition by formulating two sufficient criteria describing the smoothness of the solution and the degree of ill-posedness of the forward operator in terms of a family of subspaces. For linear deterministic inverse problems we show that variational source conditions are necessary and sufficient for convergence rates slower than the square root of the noise level. A similar result is shown for linear inverse problems with white noise. If the forward operator can be written in terms of the functional calculus of a Laplace-Beltrami operator, variational source conditions can be characterized by Besov spaces. This is discussed for a number of prominent inverse problems.

Effect of temporal resolution and serial autocorrelations in event-related functional MRI

Abstract: PURPOSE To assess the impact of colored noise on statistics in event-related functional MRI (fMRI) (visual stimulation using checkerboards) acquired by simultaneous multislice imaging enabling repetition times (TRs) between 2.64 to 0.26 s. METHODS T-values within the visual cortex obtained with analysis tools that assume a first-order autoregressive plus white noise process (AR(1)+w) with a fixed AR coefficient versus higher-order AR models with spatially varying AR coefficients were compared. In addition, dependency of T-values on correction of physiological noise (respiration, heart rate) was evaluated. RESULTS Optimal statistical power was obtained for a TR of 0.33 s, but T-values as obtained by AR(1)+w models were strongly dependent on the predefined AR coefficients in fMRI with short TRs which required higher-order AR models to achieve stable statistics. Direct estimation of AR coefficients revealed the highest values within the default mode network while physiological noise had little influence on statistics in cortical structures. CONCLUSION Colored noise in event-related fMRI obtained at short TRs originates mainly from neural sources and calls for more sophisticated correction of serial autocorrelations which cannot be achieved with standard methods relying on AR(1)+w models with globally fixed AR coefficients. Magn Reson Med 76:1805-1813, 2016. © 2016 International Society for Magnetic Resonance in Medicine.

Intermittency for the wave and heat equations with fractional noise in time

Abstract: In this article, we consider the stochastic wave and heat equations driven by a Gaussian noise which is spatially homogeneous and behaves in time like a fractional Brownian motion with Hurst index H>1/2. The solutions of these equations are interpreted in the Skorohod sense. Using Malliavin calculus techniques, we obtain an upper bound for the moments of order p≥2 of the solution. In the case of the wave equation, we derive a Feynman–Kac-type formula for the second moment of the solution, based on the points of a planar Poisson process. This is an extension of the formula given by Dalang, Mueller and Tribe [Trans. Amer. Math. Soc. 360 (2008) 4681–4703], in the case H=1/2, and allows us to obtain a lower bound for the second moment of the solution. These results suggest that the moments of the solution grow much faster in the case of the fractional noise in time than in the case of the white noise in time.

A Robust Speaker Identification System Using the Responses from a Model of the Auditory Periphery

Abstract: Speaker identification under noisy conditions is one of the challenging topics in the field of speech processing applications. Motivated by the fact that the neural responses are robust against noise, this paper proposes a new speaker identification system using 2-D neurograms constructed from the responses of a physiologically-based computational model of the auditory periphery. The responses of auditory-nerve fibers for a wide range of characteristic frequency were simulated to speech signals to construct neurograms. The neurogram coefficients were trained using the well-known Gaussian mixture model-universal background model classification technique to generate an identity model for each speaker. In this study, three text-independent and one text-dependent speaker databases were employed to test the identification performance of the proposed method. Also, the robustness of the proposed method was investigated using speech signals distorted by three types of noise such as the white Gaussian, pink, and street noises with different signal-to-noise ratios. The identification results of the proposed neural-response-based method were compared to the performances of the traditional speaker identification methods using features such as the Mel-frequency cepstral coefficients, Gamma-tone frequency cepstral coefficients and frequency domain linear prediction. Although the classification accuracy achieved by the proposed method was comparable to the performance of those traditional techniques in quiet, the new feature was found to provide lower error rates of classification under noisy environments.

Interpretation of the auto-mutual information rate of decrease in the context of biomedical signal analysis

Abstract: The mutual information (MI) is a measure of both linear and non-linear dependences. It can be applied to a time series and a time-delayed version of the same sequence to compute the auto mutual information function (AMIF). Moreover, the AMIF rate of decrease (AMIFRD) with increasing time delay in a signal is correlated with its entropy and has been used to characterise biomedical data. In this paper, we aimed at gaining insight into the dependence of the AMIFRD on several signal processing concepts and at illustrating its application to biomedical time series analysis. Thus, we have analysed a set of synthetic sequences with the AMIFRD. The results show that the AMIF decreases more quickly as bandwidth increases and that the AMIFRD becomes more negative as there is more white noise contaminating the time series. Additionally, this metric detected changes in the non-linear dynamics of a signal. Finally, in order to illustrate the analysis of real biomedical signals with the AMIFRD, this metric was applied to electroencephalogram (EEG) signals acquired with eyes open and closed and to ictal and non-ictal intracranial EEG recordings.