Independent Noise Sources Research Articles

Constructive role of noise: Fast fluctuation asymptotics of transport in stochastic ratchets.

The constructive role of random fluctuations is studied in the context of transport in stochastic ratchets. We discuss the interplay of independent white (thermal) and discrete (external) noises and their generation of transport in anisotropic potentials. The constructive cooperation of such fluctuations is most apparent in the asymptotic limit of fast discrete-valued noise, a limit which presents some interesting mathematical features. We describe the asymptotic analysis of the current in the limit of fast external noise, pointing out the strong qualitative dependence of the current on the interplay of the independent noise sources and its surprising sensitivity to the regularity of the underlying anisotropic ratchet potential. (c) 1998 American Institute of Physics.

An optoelectronic CMOS circuit implementing a simulated annealing algorithm

An original optoelectronic implementation of simulated annealing is presented. A compact and simple optical system provides a chip with arrays of independent random noise sources. The silicon chip is composed of a mesh of computing cells. Each cell includes both analog and digital circuits and includes two photosensors. A detailed analysis of this cell is given including a presentation of the design constraints. A 4/spl times/4-cells prototype chip was implemented in a 1 /spl mu/m CMOS digital technology and was successfully operated at 20000 iterations per second. The measurements and characterization of this chip made possible the successful design of a 600-cells chip also presented. These results demonstrate the video-rate application of simulated annealing to early vision tasks.

Analysis of Noise due to Disturbing Inputs Varying as a Function of Time, Frequency and Space.

Information processing equipment such as a copy machine, which contains motors, generates vibration and noise varying as a function of time, frequency and space in a cycle. This mechanism cannot be analyzed by conventional spectrum analysis using time and space averages, because a transient state occurs. In this research, by applying short time principal component analysis, the number of independent vibration and noise sources is extracted from the signals of acceleration pickups and microphones. These results show the change of vibration and noise sources, including external noise, in a cycle. Vibration and sound pressure patterns can be expressed continuously, based on measurement or prediction by the boundary element method using vibration data on the surface of the structure in each instance. Moreover, transient external noise can be separated from vibrationally induced noise in practice.

Monument motion and measurements of crustal velocities

It is usually assumed in geodetic studies that measurement errors are independent from one measurement to the next and that the rate of deformation (velocity) is constant over the duration of the experiment. Any temporal correlation between measurements can substantially affect the uncertainty in this velocity estimate when it is determined from the time series of measurements. One source of possible long‐term correlation is motion of the geodetic monument with respect to the “deep” crust. Available measurements suggest that this motion introduces errors that have the form of a random walk process. We show how such errors affect the uncertainty of velocity estimates. For a geodetic experiment of set duration we calculate the velocity uncertainty as a function of the number of observations and of the relative amount of correlated and uncorrelated noise. We find that 1) neglecting long‐term temporal correlations makes the uncertainty in the estimated velocities much too small, and that 2) when the correlated and independent noise sources are of similar magnitude, the expected improvement in uncertainty from having more measurement is not realized; there is almost no improvement in some cases. We have also examined the effect of outliers (“blunders”) on the velocity uncertainty; for a frequency of outliers typical of geodetic field campaigns, the previous two conclusions remain unchanged. These results suggest that long‐term correlations have a large effect on estimating deformation rates; unless these correlations are small, frequent observations give little advantage. If frequent observations are planned, the amount of correlated noise due to monument instability must be kept small if the full capabilities of the measurement technique are to be realized.

Scalable array of Gaussian white noise sources foranalogue VLSI implementation

A novel method for generating arrays of Gaussian white noise sources is described. Arrays of binary pseudorandom generators are obtained using a cellular automaton, and each binary source is converted into an independent Gaussian noise source. An electronic implementation is described.

Acoustic intensity measurements in the presence of low Mach number flow

Abstract : Acoustic intensity is an important analysis tool since it provides wave propagation directionality along with absolute magnitude, and it can be measured in the near or far field of a source. Acoustic intensity measurements acquired in the presence of a mean flow are susceptible to errors due to the effects of the flow noise on the sensor. To determine if this error could be accurately quantified, intensity measurements were acquired, with the standard two microphone cross spectral technique, in a sound field that contained both mean flow and an independent random broadband noise source. The microphones were flush mounted, at several different separation distances, in the test section of a wind tunnel that provided the desired flow conditions, while a large speaker provided the independent random noise source. The error calculations were based on a technique that had already been derived theoretically and published, but had not been proven experimentally. The experiments performed validate that the error is indeed a bias error and that it can be accurately quantified. In addition, accurate quantification of the error is not limited to one-dimensional sound fields that contain only plane waves, and the method can be easily extended to tow or three directions with complex wave propagation. Acoustic intensity, Low mach number, Flow, Two microphone, Cross spectral, Wind tunnel.

The Physical Significance of the Eigenvalues in Adaptive Arrays

We describe the physical significance of the eigenvalues associated with an adaptive antenna array. We also show how the eigenvalues are affected by the power output of the noise sources, the location of the noise sources, and the spatial configuration of the array antenna. The model used to show these relationships consists of two array elements and two independent noise sources located in the far field. We show how the eigenvalues of the covariance matrix vary with the angle of incidence of the noise sources.

Stochastic resonance in two coupled bistable systems

We consider the collective response of two coupled bistable oscillators driven by independent noise sources to a periodical force. We have found that there exists an optimal value of the coupling strength for which the signal-to-noise ratio of the collective response has its maximal value. The connection of this effect with the phenomenon of stochastic synchronization is established.

Electrical model for high-power-density laser diodes

We present an electrical model for modulation and noise of laser diodes that takes spectral-hole burning into account and, unlike previous models, is accurate at the quantum level. The active part of the laser diode is represented by a capacitance-expressing carrier storage and a series resistance 1 + β, where β is proportional to the spectral-hole depth. These two elements are followed by a negative impedance converter. The modulation rate measured on this electrical model is in excellent agreement with the theoretical expression. Amplitude noise is simulated by two independent noise sources whose spectral densities are independent of the nonlinearity.

Low-frequency noise of Schottky diodes operating under DC bias and as hf and vhf detectors

A Schottky diode (SD) is represented by an equivalent circuit containing two parallel-connected diodes characterizing the properties of the inner and outer regions of the diode. A noise model of an SD is examined that includes four mutually independent hf noise sources localized in the junctions and base resistances of the inner and outer diodes. The model explains the diverse dependences of SD noise on current, temperature, and coefficient of ideality as well as the noise behavior of SDs operating as hf and vhf detectors.

Solid-state shot noise.

Shot noise and thermal-equilibrium noise are often, and incorrectly, viewed as additive and independent noise sources. The two forms of noise can even be identical, as recognized by several pionering investigators long ago. Shot noise measures the graininess of the conduction process, and in samples with a fixed number of carriers, where the mean free path is short compared to the sample length, it is determined by the passage of a carrier through its mean free path. For a classical nondegenerate conductor we show that shot noise calculated that way is the thermal-equilibrium current. For mesoscopic conductors that transmit elastically with a probability small compared to unity, thermal-equilibrium noise is also shown to be approximately the sum of two shot-noise terms, one for the arriving stream at each reservoir. For a semiclassical metallic conductor, at zero temperature, the noise proportional to current flow is shot noise related to the charge transferred between sample electrodes, when a carrier goes through a mean free path. At higher temperatures, a suggestive physical argument is used to show that noise increases above thermal-equilibrium noise according to the square of the ratio of the energy gained in one mean free path, to the thermal energy.

Noise and detection limits of indirect absorption detection in capillary zone electrophoresis

The factors which contribute to the noise and signal in indirect absorption detection in capillary zone electrophoresis are studied. Two independent noise sources, the visualization agent and the detector, are distinguished. The noise from the visualization agent can be affected by the applied voltage, the surface modification of capillaries and the concentration of the visualization agent. A new factor named the “noise coefficient” is found which represents the contribution to the noise from the visualization agent. The physical interpretation of the noise coefficient is the ratio of the concentration fluctuation to the concentration of the visualization agent. A new equation that correlates detection limits with molar absorptivity and concentration of the visualization agent, noise coefficient and instrument noise is proposed, and the functions of those factors are discussed.

Signal-to-noise power or signal-to-noise energy for maximizing decision performance?

In our tutorial on preprocessing, we have provided insight into the importance of preamplification for combating system noise. We have also shown that it is the energy, and not necessarily the power, in the signal that determines the performance of a processor algorithm. A future article will cover the whitening process when the noise has certain correlation characteristics, i.e., colored. There will also be a discussion on the difference between independent sources of noise and eigenvectors which show up in noise covariance matrices.

Order statistic distributions with multiple windows

Algorithms for computing the distributions of order statistic related estimators with moving or multiple windows are presented. These algorithms may be used to compute joint distributions of moving window estimators, such as moving median filters, or of estimators made from ranking operations on multiple windows, such as many stacked or morphological filters. The presented algorithms make no distributional assumptions on the underlying random variables, but do make assumptions on the dependency between them. For instance, the random variables may be independent, Markov, or Markov-corrupted by an independent noise source. Unlike other approaches, these algorithms have polynomial complexity in the number of random variables. How these algorithms may be easily implemented is shown. Finally, two computational examples of the behavior of median filters are given. >

Interaural correlation discrimination and autocorrelation

The discrimination of differences in interaural correlation was examined for auditory noise sources differing internally in terms of their autocorrelation. Interaural correlation discrimination is inversely related to the autocorrelation of the sound source: lowest interaural thresholds with independent random noise sources; highest thresholds with repeated periodic noise sources. Interaural thresholds increase with higher periodicities. Periodicity leads to higher thresholds, apparently, by reducing the number of independent samples for the calculation of interaural correlation.

Lateralization and interaural correlation

The lateralization of ongoing interaural delays for broadband noise is necessarily related to the interaural correlation of the noise. (Ongoing delays between independent noise sources cannot be defined. Thresholds for interaural delays may be obtained by simply manipulating the interaural correlation.) A possible interpretation of the poorer lateralization at long interaural delays is that the interaural correlation of the presented signal is reduced, perhaps as the result of greater internal noise associated with longer delays. A weak test of this interpretation is to examine the discrimination of interaural correlations at different interaural delays. The course of discrimination thresholds for interaural correlation closely follows the course of thresholds for longer interaural delays.

Boundary layer flow noise—The direct radiation

The farfield sound radiation due to the transitional and turbulent boundary layer flow over a rigid, finite body of revolution is addressed quantitatively. Three statistically independent sources of flow noise are analyzed; namely, the intermittent laminar-to-turbulent transition zone that occurs near the nose, the fully developed turbulent boundary layer that covers nearly all of the body surface, and the unsteady trailing edge flow that occurs on the body stabilizer fins. The modeling is used to predict the radiated noise spectra measured in a deep lake along the trajectory of a test body that was released from the bottom and propelled by buoyancy. These experimental data are from the Huddle and Skudrzyk [J. Acoust. Soc. Am. 46, 130–157 (1969)] flow noise experiments. In these experiments the radiated noise was found to be independent of the body composition (both metal and wooden units were used) and the authors concluded that flow unsteadyness was the primary source of farfield radiation. The predictions presented here support that conclusion in that the transition zone and trailing edge flows are very unsteady and their acoustic emissions are significantly more intense than those from the relatively stable turbulent boundary layer flow. [ Work supported by Applied Research Laboratory under contract with U. S. Navy.]

On the properties of reduced order Kalman filters

Several known results are unified by considering properties of reduced-order Kalman filters. For the case in which the number of noise sources equals the number of observations, it is shown that the reduced-order Kalman filter achieves zero steady-state variance of the estimation error if and only if the plant has no transmission zeros in the right-half plane, since these would be among the poles of the Kalman filter. The reduced-order Kalman filter cannot achieve zero variance of the estimation error if the number of independent noise sources exceeds the number of observations. It is also shown that the reduced-order Kalman filter achieves the generalized Doyle-Stein condition for robustness when the noise sources are colocated with the control inputs. When there are more observations than noise sources, additional noise sources can be postulated to improve the observer frequency response without diminishing robustness.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Active noise control on systems with time-varying sources and acoustical elements

An active noise control system has been developed based on a system identification concept using a recursive adaptive filter to model the direct and feedback elements of an acoustic system. An independent random noise source is used with a second adaptive filter to provide a model of the output transducer and error path transfer functions. This system has the ability to continuously cancel narrow band and broadband noise. The system identification configuration combined with adaptive filter techniques enables the system to respond quickly and accurately to changes in time-varying sources, such as frequency or amplitude, and changes in the acoustical system, such as temperature. Noise reduction results will be presented. The system capabilities will be demonstrated on a variety of time-varying sources and time-varying acoustical elements. The ability of the system to track these changes in real-time as well as implications for actual applications will be discussed.

Upper bound on the rate of entropy increase accompanying noise power flow through linear systems

An upper bound is established for the rate of entropy increase due to noise power flow in a nonisothermal linear network containing n independent noise sources. The bound depends on the net power flows to (or from) the noise sources collectively, the lowest noise temperature in the network, and the efficiency of a Carnot heat engine operating between the highest and the lowest noise temperature occurring in a system. The author's example demonstrates that for a two port, the upper bound is actually reached and therefore a tighter bound cannot be found in general. Based on this example, a previously published bound is interpreted as the statement that the rate of entropy increase in the given n-port system cannot exceed that in a two port, in which the terminations are at the maximum and the minimum temperatures and the power flow equal the net value.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>