Showing papers on "White noise published in 1981"
TL;DR: In this article, a differential equation model for hysteretic systems with strength, stiffness or combined degradation is presented, without recourse to the Krylov-Bogoliubov approximation.
Abstract: A differential equation model for hysteretic systems with strength, stiffness or combined degradation is presented. Solution under white noise, Kanai filtered white noise and temporally modulated filtered white noise is obtained by equivalent linearization, without recourse to the Krylov-Bogoliubov approximation typically required for hysteretic systems. Resulting zero time lag covariance response matrices agree well with simulated solutions at all excitation levels. First passage predictions are nonconservative, because of the non-Gaussian character of the response.
414 citations
TL;DR: In this paper, a digital computer simulation of adaptive closed-loop control for a specific application, sound cancellation in a duct, is presented, which is an extension of Sondhi's adaptive echo canceler and Widrow's adaptive noise canceler from signal processing to control.
Abstract: Most active sound cancellation systems reported in the literature use open‐loop control, depend on near‐zero phase delay in control system elements, and require constant acoustic signal transit time from a signal pickup (microphone) to a control sound source (loudspeaker). The applicability of such systems can be significantly enhanced by using closed‐loop control. This study concerns a digital computer simulation of adaptive closed‐loop control for a specific application, sound cancellation in a duct. The key element is an extension of Sondhi’s adaptive echo canceler and Widrow’s adaptive noise canceler from signal processing to control. The adaptive algorithm is thus based on the LMS gradient search method. The simulation shows that one or more pure tones can be canceled down to the computer bit noise level (−120 dB). In the presence of additive white noise, pure tones can be canceled to at least 10 dB below the noise spectrum level for SNR’s down to at least 0 dB. The underlying theory implies that the algorithm allows tracking tones with amplitudes and frequencies that change more slowly with time than the adaptive filter adaptation rate. The theory implies also that the method can cancel narrow‐band sound in the presence of spectrally overlapping broadband sound. The method can be applied more widely, particularly to control systems that involve transport delay.
382 citations
TL;DR: In this paper, an autoregressive (AR) model was used to analyze the optical light curve of the quasar 3C 273, and the best AR model was determined from sampled data and transformed to an MA for interpretation.
Abstract: Random process models phased in the time domain are used to analyze astrophysical time series data produced by random processes. A moving average (MA) model represents the data as a sequence of pulses occurring randomly in time, with random amplitudes. An autoregressive (AR) model represents the correlations in the process in terms of a linear function of past values. The best AR model is determined from sampled data and transformed to an MA for interpretation. The randomness of the pulse amplitudes is maximized by a FORTRAN algorithm which is relatively stable numerically. Results of test cases are given to study the effects of adding noise and of different distributions for the pulse amplitudes. A preliminary analysis of the optical light curve of the quasar 3C 273 is given.
284 citations
TL;DR: A new technique for modelling the signal and the measurements is developed based on Kalman Filtering theory for the optimal estimation of the 60 Hz information and results indicate that the technique converges to the true 60 Hz quanitities faster than other algorithms that have been used.
Abstract: During the first cycle following a power system fault, a high speed computer relay has to make a decision usually based on the 60 Hz information, which is badly corrupted by noise The noise in this case is the nonfundamental frequency components in the transient current or voltage, as the case may be For research and development purposes of computer relaying techniques, the precise nature of the noise signal is required The autocorrelation function and variance of the noise signal was obtained based on the frequency of occurrence of the different types of faults, and the probability distribution of fault location A new technique for modelling the signal and the measurements is developed based on Kalman Filtering theory for the optimal estimation of the 60 Hz information The results indicate that the technique converges to the true 60 Hz quanitities faster than other algorithms that have been used The new technique also has the lowest computer burden among recently published algorithms and appears to be within the state of the art of current microcomputer technology
146 citations
TL;DR: In this paper, a random model of fault motion in an earthquake is formulated by assuming that the slip velocity is a random function of position and time truncated at zero, so that it does not have negative values.
Abstract: A random model of fault motion in an earthquake is formulated by assuming that the slip velocity is a random function of position and time truncated at zero, so that it does not have negative values. This random function is chosen to be self-affine; that is, on change of length scale, the function is multiplied by a scale factor but is otherwise unchanged statistically. A snapshot of slip velocity at a given time resembles a cluster of islands with rough topography; the final slip function is a smoother island or cluster of islands. In the Fourier transform domain, shear traction on the fault equals the slip velocity times an impedance function. The fact that this impedance function has a pole at zero frequency implies that traction and slip velocity cannot have the same spectral dependence in space and time. To describe stress fluctuations of the order of 100 bars when smoothed over a length of kilometers and of the order of kilobars at the grain size, shear traction must have a one-dimensional power spectrum is space proportional to the reciprocal wave number. Then the one-dimensional power spectrum for the slip velocity is proportional to the reciprocal wave number squared and for slip to its cube. If slip velocity has the same power law spectrum in time as in space, then the spectrum of ground acceleration will be flat (white noise) both on the fault and in the far field.
127 citations
TL;DR: In this paper, a model of a passive nerve cylinder undergoing random stimulus along its length is proposed, and the model is approximated by the solution of a stochastic partial differential equation.
Abstract: We propose a model of a passive nerve cylinder undergoing random stimulus along its length. It is shown that this model is approximated by the solution of a stochastic partial differential equation. Numerous properties of the sample paths are derived, such as their modulus of continuity, quadratic and quartic variation, and it is shown that the solution exhibits the phenomenon of flicker noise. The first-passage problem is studied, and it is shown to be connected with a first-hitting time for an infinite-dimensional diffusion.
118 citations
TL;DR: In this article, a simulation comparing the smoothed coherence transform and maximum likelihood estimation methods to the basic cross correlation technique for time delay estimation is presented. And the variance of the time delay estimates are compared to the minimum variance obtainable in theory as given by the Cramer-Rao lower bound.
Abstract: The time delay between signals received at two (or more) sensors has proven to be a useful parameter in passive sonar for estimating the location of an acoustic source. This paper presents the results of a simulation comparing the smoothed coherence transform and maximum likelihood estimation methods to the basic cross correlation technique for time delay estimation. Band-limited random signals which are corrupted by white noise and received at two sensors are considered at various signal-to-noise ratios. The variance of the time delay estimates are compared to the minimum variance obtainable in theory as given by the Cramer-Rao lower bound.
82 citations
TL;DR: In this paper, an adaptive nonlinear Kalman-type filter is presented for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise.
Abstract: An adaptive nonlinear Kalman-type filter is presented for the restoration of two-dimensional images degraded by general image formation system degradations and additive white noise. A vector difference equation model is used to model the degradation process. The object plane distribution function is partitioned into disjoint regions based on the amount of spatial activity in the image, and difference equation models are used to characterize this nonstationary object plane distribution function. Features of the restoration filter include the ability to account for the response of the human visual system to additive noise in an image; a two-dimensional interpolation scheme to improve the estimates of the initial states in each region; and a nearest neighbor algorithm to choose the previous state of vector for the state of pixel (i,j).
75 citations
TL;DR: Conditions for uniform asymptotic stability in the large of the optimal minimum mean square error linear filter are developed for linear systems whose observations are corrupted by white multiplicative noise in addition to white additive noise.
Abstract: Conditions for uniform asymptotic stability in the large of the optimal minimum mean-square error linear filter are developed for linear systems whose observations are corrupted by white multiplicative noise in addition to white additive noise. Both discrete-time as well as continuous-time systems are considered. The multiplicative noise model may be useful in problems associated with phenomena such as fading, or reflection of the transmitted signal from the ionosphere, and also certain situations involving sampling, gating, or amplitude modulation. Conditions for existence, uniqueness, and stability of the steady-state optimal filter are also considered for time-invariant systems.
66 citations
TL;DR: In this article, a simple, deterministic, dynamical system for sea ice extent, deep-ocean temperature, and atmospheric carbon dioxide that yields a stable limit cycle as a solution is presented.
Abstract: Based on a more detailed model developed previously, governing possible feedbacks between sea ice extent (η), deep-ocean temperature (θ), and atmospheric carbon dioxide, we have constructed a simple, deterministic, dynamical system for η and θ that yields a stable limit cycle as a solution. To make the system more realistic we add random (white noise) forcing and explore the new response as a function of the amplitude of this stochastic forcing. Included in the analysis are examples of sample time series, sample phase trajectories, variance spectra, and “residence density” in the phase space. The results show that physically reasonable values of the stochastic amplitude do not completely obscure the basic limit cycle, but they do convert an intransitive, deterministic system to an almost-intransitive one that tends to reside longer in two distinct regions of the phase space, with relatively fast transitions between thorn. The solutions also show how stochastic forcing of one component of the clim...
58 citations
TL;DR: In this paper, the authors describe and discuss a paper of T.N. Thiele from 1880 where he formulates and analyses a model for a time series consisting of a sum of a regression component, a Brownian motion and a white noise.
Abstract: Summary We describe and discuss a paper of T.N. Thiele from 1880 where he formulates and analyses a model for a time series consisting of a sum of a regression component, a Brownian motion and a white noise. He derives a recursive procedure for estimating the regression component and predicting the Brownian motion. The procedure is now known as Kalman filtering. He estimates the unknown variances of the Brownian motion and the white noise by an iterative procedure that essentially is the EM-algorithm. We finally give a short account of an application of Thiele's model and method to the description of hormone production during normal pregnancy.
TL;DR: In the presence of internal noise the variables describing a system are intrinsically stochastic as mentioned in this paper, and the question whether the equation has to be interpreted according to Ito or Stratonovich concerns these higher orders, for which the equation is not valid anyway.
Abstract: In the presence of internal noise the variables describing a system are intrinsically stochastic. If they constitute a Markov process the Ω expansion enables one to extract a deterministic macroscopic equation and to compute the fluctuations in successive approximations. In the lowest or linear noise approximation the fluctuations can be represented by a Langevin equation, provided it is handled appropriately. Higher orders cannot be described by any white noise Langevin equation. The question whether the equation has to be interpreted according to Ito or Stratonovich concerns these higher orders, for which the equation is not valid anyway.
TL;DR: In this article, a model for the spectrum of the noise produced by passing a signal through a uniform quantizer is presented, which requires knowledge only of the amplitude distribution of the derivative of this signal.
Abstract: A model is given for the spectrum of the noise produced by passing a signal through a uniform quantizer. The model requires knowledge only of the amplitude distribution of the derivative of this signal. The model is compared with experimental results for a sinusoidal input signal and the sum of two sinusoids. Conditions are given under which the quantization noise spectrum is white.
TL;DR: In this paper, the authors take the view that a time series model, linear or not, is judged adequate only if it reduces the observed data to approximate Gaussian white noise, and study the goodness of fit of self-exciting threshold autoregressive models (SETAR) from this standpoint.
Abstract: SUMMARY We take the view that a time series model, linear or not, is judged adequate only if it reduces the observed data to approximate Gaussian white noise. We study the goodness of fit of self-exciting threshold autoregressive models (SETAR) from this standpoint. We also study the practical utility of the instantaneous Box-Cox transformation as an aid to facilitate the desired reduction. Multi-step-ahead predictions of the Wolf s sunspot numbers are given for the years 1980 to 1987.
TL;DR: In this paper, the authors considered the problem of finite-dimensional recursive filters in the nonlinear case, where the signal is a diffusion process and the observations are corrupted by additive white noise.
Abstract: The paper deals with a possible approach to the problem of finite-dimensional filters in the nonlinear case, when the signal is a diffusion process and the observations are corrupted by additive white noise. The approach considers a sequence of finite-dimensional recursive filters that approximate the actual optimal one. The approximating filters are given in terms of functionals of continuous-time Markov chains that converge weakly to the original diffusion. These functionals can be recursively computed via a finite-dimensional Zakai equation, for which the solution is given in terms of a robust input-output relation.
01 Apr 1981
TL;DR: In this paper, the initial conditions of the filter are set so that the output process will be stationary, and the Levinson-Durbin algorithm provides an efficient means for determining these initial conditions.
Abstract: A new technique is presented for efficiently generating colored noise. Instead of discarding initial samples to account for the transient, the approach proposed here is to set the initial conditions of the filter so that the output process will be stationary. It is shown that the Levinson-Durbin algorithm provides an efficient means for determining these initial conditions.
01 Jan 1981
TL;DR: This chapter describes the approaches and results of input design in the engineering literature over the past two decades, which has been toward more general models, more realistic criteria, better understanding of the nature of the optimal inputs, and the development of more efficient computational methods.
Abstract: Publisher Summary This chapter describes the approaches and results of input design in the engineering literature over the past two decades. The progression has been toward more general models, more realistic criteria, better understanding of the nature of the optimal inputs, and the development of more efficient computational methods. All of these developments have led to a stage at which applications to a number of practical problems are within the state of the art. The first systematic attempt at obtaining an optimal input seems to have been that of Levin (1960), who considers estimation of the impulse response function of a discrete-time single-input single-output (SISO) linear system in the presence of white measurement noise. Levin shows that the optimal energy or amplitude-constrained input that minimizes the trace or the determinant of the covariance matrix is a white noise sequence.
TL;DR: Thresholds for the speech signal were comparable across all infant groups for both levels of masking noise and adult thresholds were approximately 10-12 dB lower than those of infants at both masking levels.
Abstract: Localization responses to a speech phrase masked by white noise were obtained from infants 6, 12, 18, and 24 months of age and from adults. The masking noise was presented continuously from two lou...
TL;DR: In this paper, the spectrum of a sampled 1st-order low-pass filtered white noise is calculated, and theoretical results are compared with measurements made on a laboratory model, and the effect of undersampling appears clearly for noise bandwidths exceeding the sampling rate.
Abstract: In the letter, the spectrum of a sampled 1st-order lowpass filtered white noise is calculated, and theoretical results are compared with measurements made on a laboratory model. In this context, the effect of undersampling appears clearly for noise bandwidths exceeding the sampling rate. This analysis contributes to the study of noise in switched capacitor networks.
TL;DR: The basis of the method is the Linear Prediction Theory (LPT) which has been extensively used in processing digital data in other technical fields and is discussed.
Abstract: Most of the currently used algorithms for numerical generation of sea wave records which are compatible with a specified power spectrum are based on the super-position of several harmonic waves. This article presents an alternative method of simulation. The basis of the method is the Linear Prediction Theory (LPT) which has been extensively used in processing digital data in other technical fields. Specifically, records of sea waves which are compatible with the target spectrum are obtained as the output of a recursive digital filter to a white noise input. A procedure for determining the filter parameters is discussed. Several numerical examples are presented.
20 May 1981
TL;DR: In this paper, a unified approach is applied to the derivation of a number of formulas for the probability of signal detection and probability of false alarm in incoherent integration, with fluctuating signal-to-noise ratios and/or fluctuating thresholds.
Abstract: : A unified approach is applied to the derivation of a number of formulas for the probability of signal detection and the probability of false alarm. The context is incoherent integration, with fluctuating signal-to-noise ratios and/or fluctuating thresholds. The standard results are obtained and extended to more general fluctuation models. A fundamental duality is established between fluctuating signals and fluctuating thresholds and used to simplify the derivations. Also included is an expression of the cumulative F-distribution as a finite sum of Marcum Q-functions.
TL;DR: In this article, the authors studied the quantum motion of a particle in a fluctuating lattice on the basis of a time-dependent Hamiltonian with site energies being randomly modulated by stochastic noises.
Abstract: Quantum motion of a particle in a fluctuating lattice is studied on the basis of a time-dependent Hamiltonian with site energies being randomly modulated by stochastic noises. The case of the two-state jump noise is studied in details. It is found that the particle moves diffusively on a long time scale. When the noise has a non-white spectrum, the diffusion constant is substantially enhanced in comparison with the white noise limit owing to the local coherence of the wavefunction of the particle. A numerical study is also carried out for one-dimensional cases. The analytical result is in rough agreement with the numerical calculation.
TL;DR: In this paper, the authors make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes, frequencies, and damping factors, and the associated modal decomposition is appropriate for both continuous and discrete components of the spectrum.
Abstract: Parametric methods of spectrum analysis are founded on finite-dimensional models for covariance sequences. Rational spectrum approximants for continuous spectra are based on autoregressive (AR), moving average (MA), or autoregressive moving average (ARMA) models for covariance sequences. Line spectrum approximants to discrete spectra are based on cosinusoidal models for covariance sequences. In this paper we make the point that a wide variety of spectrum types admit to modal analysis wherein the modes are characterized by amplitudes, frequencies, and damping factors. The associated modal decomposition is appropriate for both continuous and discrete components of the spectrum. The domain of attraction for the decomposition includes ARMA sequences, harmonically or nonharmonically related sinusoids, damped sinusoids, white noise, and linear combinations of these. The parametric spectrum analysis problem now becomes one of identifying mode parameters. This we achieve by solving two modified least squares problems. Numerical results are presented to illustrate the identification of mode parameters and corresponding spectra from finite records of perfect and estimated covariance sequences. The results for sinusoids and sinusoids in white noise are interpreted in terms of in-phase and quadrature effects attributable to the finite record length.
TL;DR: In this paper, the tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target.
Abstract: Tracking accuracies for the radial component of motion are computed for a track-while-scan radar system which obtains position and rate data during the dwell time on a target These results will be of interest to persons developing trackers for pulse Doppler surveillance radars. The normalized accuracies, computed for a two state Kalman tracking filter with white noise maneuver capability, are shown to depend upon two parameters, r = 4?0/?aT2 and s = ?dT/?0. The symbols ?0 and ?d are the position and rate measurement accuracies, respectively, ?a is the standard deviation of the white noise maneuver process and T is the antenna scan time. The scalar tracking filter equations are derived and numerical results are presented. Lower steady state tracking errors plus the earlier attainment of steady state accuracies are the direct consequence of incorporating the rate measurements into the tracking filter.
TL;DR: In this article, the authors compared the performance of the Burg maximum entropy method (MEM) and the discrete Fourier transform (DFT) for threshold detection of a complex sinusoid in additive noise.
Abstract: Four simulation experiments have been carried out to compare the statistics of threshold detection of a complex sinusoid in additive noise using the Burg maximum entropy method (MEM) and the discrete Fourier transform (DFT) technique. The results indicate that, in the presence of additive white noise, the DFT consistently provides a higher signal detection probability P D and a more accurate estimate of signal frequency than the MEM. In the presence of colored noise, the DFT provides a higher P D when signal-to-noise ratio (SNR) is high, or when signal detection is carried out in the low false-alarm probability P FA region. Only in the very restricted case of low SNR together with a high P FA and the signal far away from the center of the noise band does the MEM provide a higher P D than the DFT.
TL;DR: In this paper, a nonparametric identification procedure for such systems which are usually described by a diffusion model is given in Banon (1977), (1978), where weak consistency of estimators has been obtained and simulation study has been carried out successfully.
Abstract: This paper is concerned with the nonlinear identification of dynamical systems disturbed by white noise, an important problem in control engineering. A nonparametric identification procedure for such systems which are usually described by a diffusion model is given in Banon (1977), (1978), where weak consistency of estimators has been obtained and simulation study has been carried out successfully. In this paper, we prove a stronger result concerning asymptotic properties of the estimators of the drift term, namely, strong consistency, and also related results.
TL;DR: Conditions are given under which the two implementations are essentially equivalent for white noise inputs so that the frequency- domain algorithm can be used to predict the mean, variance, time response, and MSE of the time-domain algorithm.
Abstract: Adaptive cancelling can be performed in the frequency domain with significant computational savings over time-domain implementations. This paper considers the statistical behavior of a frequency-domain adaptive canceller with white noise inputs, and develops expressions for the mean and variance of the adaptive filter weights, and for the mean-square error (MSE). These are compared to the behavior of a time-domain canceller with the same inputs through a combination of analysis and simulation. It is shown that the performance of the two algorithms can differ significantly due to the effects of block processing in the FFT. However, conditions are given under which the two implementations are essentially equivalent for white noise inputs so that the frequency-domain algorithm can be used to predict the mean, variance, time response, and MSE of the time-domain algorithm.
TL;DR: In this paper, a white noise source together with a digital signal analyzer is used for measuring the impedance of power system ground systems where, because of a significant reactive component or the presence of large residual power system voltage, conventional ground resistance measuring instruments cannot be used.
Abstract: A new method is described for measuring the impedance of power system ground systems where, because of a significant reactive component or the presence of a large residual power system voltage, conventional ground resistance measuring instruments cannot be used. A white noise source together with a digital signal analyzer are used. Results of three applications are given.
01 Apr 1981
TL;DR: This paper considers an application of spectral estimation to adaptive restoration of images degraded by additive white noise by comparing three adaptive techniques of restoration.
Abstract: In this paper we consider an application of spectral estimation to adaptive restoration of images degraded by additive white noise. Three adaptive techniques of restoration are compared with a non-adaptive technique. In the non-adaptive technique, the whole image is Wiener filtered by assuming a correlation model for the signal. In the adaptive methods, a) the spectral shape of the signal is kept constant, but the variance is adaptively estimated, b) the power spectrum of each block is adaptively estimated, c) the data is adaptively decorrelated in one dimension and filtered along the other.
TL;DR: Numerical simulation data regarding the statistics of the response of a non-symmetric dynamic system are presented and serve to examine the reliability of a random vibration analysis of the system, based on the technique of equivalent linearization.