White Noise Input Research Articles

Information fusion steady-state white noise deconvolution estimators with time-delayed measurements and colored measurement noises

White noise deconvolution or input white noise estimation problem has important application backgrounds in oil seismic exploration, communication and signal processing. By the modern time series analysis method, based on the Auto-Regressive Moving Average (ARMA) innovation model, under the linear minimum variance optimal fusion rules, three optimal weighted fusion white noise deconvolution estimators are presented for the multisensor systems with time-delayed measurements and colored measurement noises. They can handle the input white noise fused filtering, prediction and smoothing problems. The accuracy of the fusers is higher than that of each local white noise estimator. In order to compute the optimal weights, the formula of computing the local estimation error cross-covariances is given. A Monte Carlo simulation example for the system with 3 sensors and the Bernoulli-Gaussian input white noise shows their effectiveness and performances.

Towards identification of Wiener systems with the least amount of a priori information: IIR cases

In this paper, we investigate what constitutes the least amount of a priori information on the nonlinearity so that the linear part is identifiable in the non-Gaussian input case. Under the white noise input, three types of a priori information are considered: quadrant information, point information, and monotonic information. In all three cases, identifiability has been established, and the corresponding nonparametric identification algorithms are developed along with their convergence proofs.

Listening to the noise: random fluctuations reveal gene network parameters

The cellular environment is abuzz with noise originating from the inherent random motion of reacting molecules in the living cell. In this noisy environment, clonal cell populations show cell-to-cell variability that can manifest significant phenotypic differences. Noise-induced stochastic fluctuations in cellular constituents can be measured and their statistics quantified. We show that these random fluctuations carry within them valuable information about the underlying genetic network. Far from being a nuisance, the ever-present cellular noise acts as a rich source of excitation that, when processed through a gene network, carries its distinctive fingerprint that encodes a wealth of information about that network. We show that in some cases the analysis of these random fluctuations enables the full identification of network parameters, including those that may otherwise be difficult to measure. This establishes a potentially powerful approach for the identification of gene networks and offers a new window into the workings of these networks.

Identification of dynamic nonlinear polynomial models in the errors-in-variables framework

An approach for the identification of a class of discrete-time nonlinear polynomial single-input single-output dynamic errors-in-variables system models in the case of white input noise and white output noise is proposed. The algorithm is constructed within the extended bias compensated least squares framework. The separable nonlinear least squares method is subsequently utilised to determine the model parameters together with the input and output noise variances. A numerical Monte-Carlo simulation demonstrates the robustness of the proposed approach with regard to noise.

Decoupled Wiener state fuser for descriptor systems

By the modem time series analysis method, based on the autoregressive moving average (ARMA) innovation models and white noise estimation theory, using the optimal fusion rule weighted by diagonal matrices, a distributed descriptor Wiener state fuser is presented by weighting the local Wiener state estimators for the linear discrete stochastic descriptor systems with multisensor. It realizes a decoupled fusion estimation for state components. In order to compute the optimal weights, the formulas of computing the cross-covariances among local estimation errors are presented based on cross-covariances among the local innovation processes, input white noise, and measurement white noises. It can handle the fused filtering, smoothing, and prediction problems in a unified framework. Its accuracy is higher than that of each local estimator. A Monte Carlo simulation example shows its effectiveness and correctness.

Adaptive control for promoting synchronization design of chaotic Colpitts oscillators

This paper presents an adaptive control approach to achieve stabilization and synchronization of chaotic Colpitts oscillators. One of the pivotal control inputs was uncovered to stabilize the chaotic Colpitts oscillator. Furthermore, the robustness of adaptive synchronization in the presence of artificial perturbation of the pivotal control input and Additive White Gaussian Noise (AWGN) were both investigated using the Lyapunov method. Finally, numerical simulations show the validity of the method, due to fewer errors in synchronization.

Method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise

Neurons are subject to synaptic inputs from many other cells. These inputs consist of spikes changing the conductivity of the target cell, i.e., they enter the neural dynamics as multiplicative shot noise. Up to now, only for simplified models like current-based (additive-noise) point neurons or models with Gaussian white-noise input, exact solutions are available. We present a method to calculate the exact time-dependent moments for the voltage of a point neuron with conductance-based shot noise and a passive membrane. The exact solutions show features (for instance, maxima of the moments vs time) which are also confirmed by numerical simulations. The theoretical analysis of subthreshold membrane fluctuations may contribute to a better comprehension of neural noise in general. We also discuss how the analytical results may provide additional conditions for estimating parameters from experimental data.

Mode Superposition Method of Non Stationary Seismic Responses for Non Classically Damped Linear Systems

The real earthquake ground accelerations are usually non stationary vibration process. In order to estimate the influence of the non stationarity of ground motion on the accuracy of modal superposition rule of complex complete quadratic combination (CCQC), a new time-dependent CCQC(t) algorithm is derived by using a determinate envelope function to modulate a stationary random white noise process and remaining other assumptions same as normal CQC method. The proposed time-dependent CCQC(t) method needs to calculate the variances, covariance, and cross variances for different modes as time functions. For CCQC(t) method, the cross variances between a pair of two different modes are usually named cross correlation coefficients and play very important role in estimation of maximum responses just as for CQC method, but in this case the cross correlation coefficients are time dependent. Moreover, CCQC(t) and CQC(t) methods need to define envelop function and to calculate the corresponding non stationary seismic response rather than CCQC and CQC methods where only stationary steady-state responses are concerned. Hence, the analyses and computations related to envelop function in CCQC(t) and CQC(t) methods also play very a important role in this article. Several closed form formulas of time-dependent variances and cross variances are derived by using integration technique developed in time domain for four popularly used envelope functions. In order to verify these closed form formulas deduced in this article, we use four different envelope functions to fit identical envelope curve of real acceleration time history and then to carry out numerical analyses for certain examples. The numerical analysis based on proposed CCQC(t) algorithm shows that all the seismic responses of the examples computed from the adopted four different envelope functions which are used to depict same envelop curve of input acceleration are almost the same. The example analyses also show that for normal structure and ground motion input the discrepancy of the maximum seismic responses calculated from CCQC(t) and CCQC methods for non classically damped linear system and that from CQC(t) and CQC methods for classically damped linear system is of insignificance because the occurrence times of the variance responses and cross covariance responses usually concentrate within very narrowed time interval and close to the peak value location of the input motion at time axis. Further analyses show that the significance of the non stationarity mainly depends on how far the peak value arrival times of the modal responses shift each other and how sharper the shape of the envelop of input motion. Generally speaking, the larger the peak values arrival time shift and the sharper the shapes of the different modal response envelops, the greater the influence of non stationarity of ground motion on the results of mode superposition based on response spectra. These results are obtained on the basis of white noise input assumption. In addition, it is also shown that if using colorful spectrum such as Kanai power spectrum density function to replace white noise to simulate the power spectrum of the input acceleration records, the results coming from both CCQC(t) and CCQC methods may be improved to certain degree.

Correlation and Synchrony Transfer in Integrate-and-Fire Neurons: Basic Properties and Consequences for Coding

We study how pairs of neurons transfer correlated input currents into correlated spikes. Over rapid time scales, correlation transfer increases with both spike time variability and rate; the dependence on variability disappears at large time scales. This persists for a nonlinear membrane model and for heterogeneous cell pairs, but strong nonmonotonicities follow from refractory effects. We present consequences for population coding and for the encoding of time-varying stimuli.

Alternative Approach to Optimal Tuning Parameter of Liquid Column Damper for Seismic Applications

A closed-form solution for the optimum tuning ratio of a liquid column damper (LCD) that is valid for damped structures subjected to generalized seismic loading is presented. The closed-form expression is based on the extension of the theory of “fixed-point” frequencies for a classical undamped structure-mass damper system to damped structure-nonlinear LCD system. For the specific case of white noise input, the values of optimum tuning ratio have been compared with those obtained from a standard expression.

Covariance analysis for active vehicle suspensions

AbstractIn this paper the covariance analysis will be extended to active suspension systems with skyhook dampers. The covariance matrix of the entire vehicle system follows from an algebraic equation, the so‐called Ljapunov matrix equation, and no integrations are required. An essential prerequisite of the covariance analysis is a white noise input process. This can always be provided by modelling the random vehicle excitation by means of a shape filter. Performance criteria are presented and appropriate design parameters are found by optimization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Covariance analyis for active vehicle suspensions

AbstractIn this paper the covariance analysis will be extended to active suspension systems with skyhook dampers. The covariance matrix of the entire vehicle system follows from an algebraic equation, the so‐called Ljapunov matrix equation, and no integrations are required. An essential prerequisite of the covariance analysis is a white noise input process. This can always be provided by modelling the random vehicle excitation by means of a shape filter. Performance criteria are presented and appropriate design parameters are found by optimization. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Information fusion white noise deconvolution estimators for time-varying systems

White noise deconvolution or input white noise estimation has a wide range of applications including oil seismic exploration, communication, signal processing, and state estimation. Based on the Kalman filtering method and the optimal information fusion rules in the linear minimum variance sense, three distributed fused white noise deconvolution estimators weighted by matrices, diagonal matrices, and scalars, are presented for the linear discrete time-varying stochastic systems with multisensor and with different local dynamic models, respectively. The accuracy of the fusers is higher than that of each local white noise estimator. They can handle the white noise fused filtering, smoothing and prediction problems, and are applicable to the multisensor systems with colored measurement noises. In order to compute the optimal weights, the new formula of computing the local estimation error cross-covariances is presented, and the steady-state white noise deconvolution fusers are also presented, which can reduce the on-line computational burden. Two Monte Carlo simulation examples for the Bernoulli–Gaussian input white noise show their effectiveness.

Damping estimation via energy-dissipation method

This paper extends an existing single-degree-of-freedom (dof) energy-dissipation scheme to identify damping parameters for multiple-dof vibration systems. The method balances the energy input of the real system against the energy dissipated in a theoretical model to develop the identification algorithms. The theoretical friction model is assumed to consist of the viscous and Coulomb damping components. The proposed algorithms are applicable in the general- and periodic-input cases. According to the numerical studies performed on periodic excitation, the mixed-frequency harmonic input is preferable to the single-frequency one. Moreover, when noise is present in the measurements, increasing the length of integration interval can be a remedy for effects of noise on estimation accuracy. Observations made on numerical study also indicate that estimation results obtained from a band-limited white-noise input are more accurate than those obtained from the periodic one. Such excitations are adopted in the experimental study in which an electrical system is investigated. The experimental results further confirm the validity and reliability of the proposed method.

Itô calculus extended to systems driven by [formula omitted]-stable Lévy white noises (a novel clip on the tails of Lévy motion)

The paper deals with probabilistic characterization of the response of non-linear systems under α -stable Lévy white noise input. It is shown that, by properly selecting a clip in the probability density function of the input, the moments of the increments of Lévy motion process remain all of the same order ( d t ) , like the increments of the Compound Poisson process. It follows that the Itô calculus extended to Poissonian input, may also be used for α -stable Lévy white noise input processes. It is also shown that, when the clip on the tails of the probability of the increments of the Lévy motion approaches to infinity, the Einstein–Smoluchowsky equation is restored. Once these concepts are outlined extension to single oscillator is readily obtained. A discussion on the proper way to perform Monte Carlo simulation is also exploited.

A Sieve Bootstrap Method for Correlation Analysis

This note presents a nonparametric sieve bootstrap method for estimating the variance of impulse response coefficients and the process steady-state gain determined via correlation analysis. The bootstrap estimates are demonstrated to be better for small samples than the analytical finite sample variance expression for the simplified form (assuming white noise input) of the Wiener-Hopf equations. Monte Carlo simulations demonstrate that solving the linear equations resulting from the Wiener-Hopf equations can result in a variance reduction.

Blind Calibration of Timing Offsets for Four-Channel Time-Interleaved ADCs

In this paper, we describe a blind calibration method for timing mismatches in a four-channel time-interleaved analog-to-digital converter (ADC). The proposed method requires that the input signal should be slightly oversampled. This ensures that there exists a frequency band around the zero frequency where the Fourier transforms of the four ADC subchannels contain only three alias components, instead of four. Then the matrix power spectral density (PSD) of the ADC subchannels is rank deficient over this frequency band. Accordingly, when the timing offsets are known, we can construct a filter bank that nulls the vector signal at the ADC outputs. We employ a parametrization of this filter bank to develop an adaptive null steering algorithm for estimating the ADC timing offsets. The null steering filter bank employs seven fixed finite-impulse response filters and three unknown timing offset parameters which are estimated by using an adaptive stochastic gradient technique. A convergence analysis is presented for the blind calibration method. Numerical simulations for a bandlimited white noise input and for inputs containing several sinusoidal components demonstrate the effectiveness of the proposed technique

A Low Delay and Fast Converging Improved Proportionate Algorithm for Sparse System Identification

A sparse system identification algorithm for network echo cancellation is presented. This new approach exploits both the fast convergence of the improved proportionate normalized least mean square (IPNLMS) algorithm and the efficient implementation of the multidelay adaptive filtering (MDF) algorithm inheriting the beneficial properties of both. The proposed IPMDF algorithm is evaluated using impulse responses with various degrees of sparseness. Simulation results are also presented for both speech and white Gaussian noise input sequences. It has been shown that the IPMDF algorithm outperforms the MDF and IPNLMS algorithms for both sparse and dispersive echo path impulse responses. Computational complexity of the proposed algorithm is also discussed.

Dynamic Testing of A/D Converters Using the Coherence Function

The problem of characterizing an A/D converter is important to manufacturers and end users. The measured characteristics provide the means to compare devices and make design choices. This paper presents a procedure for testing a pair of A/D converters that sample the same analog signal. Since both A/D converters are measuring the same signal, the portion of the measured signals that is incoherent provides an estimate of the total noise of the two devices, from which the A/D converter effective number of bits and signal-to-noise ratio can be calculated. The removal of the coherent signal requires the calculation of the coherence function, which is computed from auto- and cross-spectral densities estimated by the Welch periodogram method. Examples of the procedure are provided for various input signals, input levels, sampling rates, and (simulated) interchannel delays. The measurement examples show that for white-noise inputs, the technique is independent of input-signal level, spectral data window, and sampling rate, provided the inputs are simultaneously sampled. With sine-wave inputs, the technique can be compared to the signal-to-noise and distortion ratio test, and it is shown that coherent removal eliminates the need for an ultrapure sine-wave source. The use of data windows is shown to be detrimental, since sidelobe energy is suppressed causing loss of coherence. The technique simplifies the setup and programming requirements for A/D converter testing because it can be applied using any input signal and is based on widely accepted processing techniques. End users and manufacturers alike should have little difficulty obtaining the programming tools needed to perform the analysis

Signal modulating noise effect in bistable stochastic resonance systems and its analog simulation

The effect of signal modulating noise in bistable stochastic resonance systems was studied theoretically and experimentally. A mathematical analysis was made on the bistable stochastic resonance model with small system parameters. An analogue circuit was designed to perform the effect. The effect of signal modulating noise was shown in the analog simulation experiment. The analog experiment was conducted for two sinusoidal signals with different frequencies. The results show that there are a sinusoidal component corresponding to the input sinusoidal signal and a noise component presented as a Wiener process corresponding to the input white noise in the system output. By properly selecting system parameters, the effect of signal modulating noise can be manifested in the system output.