Showing papers on "White noise published in 1969"
2,111 citations
TL;DR: New bounds are presented for the maximum accuracy with which parameters of signals imbedded in white noise can be estimated, which are independent of the bias and include explicitly the dependence on the a priori interval.
Abstract: New bounds are presented for the maximum accuracy with which parameters of signals imbedded in white noise can be estimated. The bounds are derived by comparing the estimation problem with related optimal detection problems. They are, with few exceptions, independent of the bias and include explicitly the dependence on the a priori interval. The new results are compared with previously known results.
329 citations
TL;DR: It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussia noise, suggesting an "estimator-correlator" philosophy for engineering approximation of the optimum receiver.
Abstract: It is shown that the likelihood ratio for the detection of a random, not necessarily Gaussian, signal in additive white Gaussian noise has the same form as that for a known signal in white Gaussian noise. The role of the known signal is played by the casual least-squares estimate of the signal from the observations. However, the "correlation" integral has to be interpreted in a special sense as an Ito stochastic integral. It will be shown that the formula includes all known explicit formulas for signals in white Gaussian noise. However, and more important, the formula suggests an "estimator-correlator" philosophy for engineering approximation of the optimum receiver. Some extensions of the above result are also discussed, e.g., additive finite-variance, not necessarily Gaussian, noise plus a white Gaussian noise component. Purely colored Gaussian noise can be treated if whitening filters can be specified. The analog implementation of Ito integrals is briefly discussed. The proofs of the formulas are based on the concept of an innovation process, which has been useful in certain related problems of linear and nonlinear least-squares estimation, and on the concept of covariance factorization.
252 citations
TL;DR: Results from three experiments that employed various permutations of the aforementioned conditions are reported, and it is shown that mixing one speech train with noise (either modulated or unmodulated) induced about 3.2 dB excess masking.
Abstract: Shifts in masked spondee thresholds during several conditions of listening (monaural, homophasic, antiphasic, and with interaural time disparity) in the presence of one to four competing maskers were measured. The maskers used were white noise, white noise modulated four times per second by 10 dB with a 50% duty cycle, the same noise with 75% duty cycle, connected speech by one male talker, and connected speech by a second male talker. Results from three experiments that employed various permutations of the aforementioned conditions are reported. The findings, after equating conditions to equivalent masker levels, were four. First, the modulated noise with 50% duty cycle produced about 3.5 dB less masking than that produced by unmodulated white noise. Second, the modulated noise with 75% duty cycle allowed only about 1 dB less shift than did the unmodulated noise. Third, mixing one speech train with noise (either modulated or unmodulated) induced about 3.2 dB excess masking. This excess is here termed per...
232 citations
TL;DR: A model for human controller remnant is postulated in which remnant is considered to arise from an equivalent observation noise vector whose components are linearly independent white noise processes.
Abstract: A model for human controller remnant is postulated in which remnant is considered to arise from an equivalent observation noise vector whose components are linearly independent white noise processes. Extensive analysis of data obtained from simple manual control systems verifies that this model structure holds over a wide range of input amplitudes and bandwidths, vehicle dynamics, and display locations. When the display is viewed foveally, the component noise processes are proportional to the variances of the displayed quantities. This constant of proportionality is independent of input parameters and of vehicle dynamics.
118 citations
TL;DR: In this article, the identification of the transition matrix and statistical parameters of a discrete linear system excited by white noise is considered and estimates of these parameters are derived and shown to be strongly consistent.
Abstract: : The paper considers the identification of the transition matrix and statistical parameters of a discrete linear system excited by white noise. Estimates of these parameters are derived and shown to be strongly consistent. It is further shown that when strongly consistent estimates are used in the Kalman Filter equations that the Kalman Filter parameters and the state variable estimates so obtained are also strongly consistent. (Author)
105 citations
01 Jun 1969
TL;DR: In this article, a statistical model for roundoff noise in floating point digital filters, proposed by Kaneko and Liu, is tested experimentally for first and second-order digital filters.
Abstract: A statistical model for roundoff noise in floating point digital filters, proposed by Kaneko and Liu, is tested experimentally for first- and second-order digital filters. Good agreement between theory and experiment is obtained. The model is used to specify a comparison between floating point and fixed point digital filter realizations on the basis of their output noise-to-signal ratio, and curves representing this comparison are presented. One can find values of the filter parameters at which the fixed and the floating point curves will cross, for equal total register lengths.
69 citations
TL;DR: In this article, the power spectrum is separated into signal and noise components, and a white noise assumption is made if the noise is due to small random near surface sources, random measurement errors, and random errors in corrections for terrain and elevation.
Abstract: Second‐derivative and downward‐continuation filtering are often employed to enhance gravity and magnetic maps. Noise due to aliasing, measurement errors, and near‐surface sources can be greatly amplified and lead to erratic filter outputs which produce spurious anomalies. To prevent this undesirable occurrence, it is often necessary to smooth the data, or equivalently, to modify the response of the applied filter. By means of the Wiener filter theory it is possible to derive optimum second‐derivative and downward‐continuation filters in either the wavenumber or space domain. Application of the theory involves separating the power spectrum into signal and noise components. A white noise assumption is realistic if the noise is due to small random near‐surface sources, random measurement errors, and random errors in corrections for terrain and elevation. As a striking demonstration of the superiority of optimum filters, the effects of optimum and “ideal” filters on a synthetic gravity map are compared.
61 citations
TL;DR: In this article, the authors considered stochastic differential games in which the two controllers have available only noise-corrupted output measurements and proposed a solution to this problem under the constraint that each controller is limited to a linear dynamic system of fixed dimension for the generation of his estimate of the system state.
Abstract: Attention is given to stochastic differential games in which the two controllers have available only noise-corrupted output measurements. Consideration is restricted to the case in which the system is linear, the cost functional quadratic, and the noises corrupting the output measurements are independent, white, and Gaussian. A solution to this problem is presented under the constraint that each controller is limited to a linear dynamic system of fixed dimension for the generation of his estimate of the system state. The optimal controls are shown to satisfy a separation theorem, the optimal estimators are shown to be closely related to Kalman filters, and the various terms in the optimal cost are shown to be readily assignable to the appropriate contributing sources.
60 citations
TL;DR: In this article, the mean square response to AM random noise, considering frequency response, input excitation spectrum, etc, was investigated. And the authors proposed a mean square system for single degree of freedom (SDF) with AM random noises.
Abstract: Mechanical single degree of freedom system mean square response to AM random noise, considering frequency response, input excitation spectrum, etc
59 citations
TL;DR: The optimal deterministic inputs derived for estimating dynamic control system parameters from white observation noise show good agreement with prior work on this topic.
Abstract: Optimal deterministic inputs derived for estimating dynamic control system parameters from white observation noise
TL;DR: In this article, an artificial random force is introduced into Burgers' model equation for turbulence and the forced model equation is solved numerically as an initial value problem, where both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process.
Abstract: An artificial random force is introduced into Burgers' model equation for turbulence. This forced model equation is solved numerically as an initial‐value problem. Both the driving force and initial velocity field are assumed Gaussian and are generated by a white noise process. Many statistical properties of this model for turbulence are studied. By adjusting the external force, the turbulence can reach an equilibrium state. The velocity correlation function and energy spectrum are calculated for the equilibrium turbulence. It is found that the energy spectrum falls off as the inverse second power of the wavenumber. The velocity correlation function is similar to the result obtained in real turbulence experiments. With Gaussian random driving force and Gaussian initial velocity field, it is found that the velocity field remains very nearly Gaussian by comparing the fourth‐order velocity correlation with the quasinormal assumption. Although the process remains very nearly Gaussian, it is found that the projection of the process on the initial white noise process becomes smaller and smaller. This is to be expected, since the dynamic system is escaping from the original random base.
TL;DR: The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered and the maximum likelihood estimation procedure is assumed.
Abstract: The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered. The maximum likelihood estimation procedure is assumed. Bounds are derived for the probability of large estimation errors.
01 Nov 1969
TL;DR: A comparison of the statistical properties of low altitude atmospheric turbulence and the characteristics of presently used simulation techniques shows that these techniques do not satisfactorily account for the non-Gaussian nature of turbulence.
Abstract: : A comparison of the statistical properties of low altitude atmospheric turbulence and the characteristics of presently used simulation techniques shows that these techniques do not satisfactorily account for the non-Gaussian nature of turbulence. A non-Gaussian turbulence simulation, intended to be used in conjunction with piloted flight simulators, is developed. The simulation produces three simultaneous random processes which represent the three orthogonal gust components. The probability distribution of each component is characterized by a modified Bessel function. The rms intensity and scale length of each component are independent parameters. A general method of introducing cross spectra between components is demonstrated. The multiplication of independent random processes is used to generate each of the gust components. Gaussian white noise generators, analog multipliers, and linear filters are used throughout the simulation. A complete analog circuit diagram is presented.
TL;DR: In this article, a new identity for the resolvent of a covariance function was derived by using a result of Siegert [3] and used to obtain a simple relation between the smoothed and filtered linear least-squares estimates of a signal process in additive uncorrelated white noise.
Abstract: By using a result of Siegert [3], we derive a new identity for the “resolvent” of a covariance function. This identity is used to obtain a simple relation between the “smoothed” and “filtered” linear least-squares estimates of a signal process in additive uncorrelated white noise.
TL;DR: White noise was interrupted by a “clickless” switch and accurate pitch matches were obtained for rates of interruption to 2000 interruptions per second.
Abstract: White noise was interrupted by a “clickless” switch. Accurate pitch matches were obtained for rates of interruption to 2000 interruptions per second.
TL;DR: The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered and the maximum likelihood estimation procedure is assumed.
Abstract: The problem of estimating the position of a position-modulated rectangular pulse in additive white noise is considered. The maximum likelihood estimation procedure is assumed. Bounds are derived for the probability of large estimation errors.
TL;DR: In this article, the estimation of completely unknown signals is studied and a sampled-data linear filter is found which estimates the signals at discrete points in time and the estimate is optimum in the sense that it is unbiased and the variance of estimate is minimized.
Abstract: The estimation of completely unknown signals is studied. Signals which have no probabilistic structure propagate through a linear system. The output of the linear system is observed in the presence of white noise. A sampled-data linear filter is found which estimates the signals at discrete points in time. The estimate is optimum in the sense that it is unbiased and the variance of the estimate is minimized (Fisher estimate).
TL;DR: Asymptotically tight upper and lower error bounds are obtained for orthogonal signals in additive white Gaussian noise channels for a class of generalized decision strategies, which afford the possibility of erasure or variable-size list decoding.
Abstract: For a class of generalized decision strategies, which afford the possibility of erasure or variable-size list decoding, asymptotically tight upper and lower error bounds are obtained for orthogonal signals in additive white Gaussian noise channels. Under the hypothesis that a unique signal set is asymptotically optimal for the entire class of strategies, these bounds are shown to hold for the optimal set in both the white Gaussian channel and the class of input-discrete very noisy memoryless channels.
TL;DR: Two estimates of prefiltered signal- noise levels are proposed, one based on r and an a priori estimate (from noise-only data) of equivalent white-noise bandwidth, the other using r and λ.
TL;DR: In this paper, a single-mode and two-mode stochastic models are developed to permit prediction of random-type ground motions and the induced response statistics of structures, based on modal contributions.
Abstract: Presented are analytic results of study on site properties and their use in ground-motion prediction and simulation. Spectral simulations of random-type ground motions based on modal contributions are formulated. Linear filters representing ground transfer characteristics of seismic stations are investigated. Single-mode and two-mode stochastic models are developed to permit prediction of random-type ground motions and the induced response statistics of structures. From the viewpoint of stochastic simulation, the autocorrelation function or the power spectral density function derived from the recorded accelerogram can be used to characterize the specific ground motion. By matching the power spectral density function of an existing ground-motion record to that of the appropriate output of a linear single- (or multi-) degree-of-freedom system subject to white noise, the predominant modal ground frequencies and dampings can be determined.
TL;DR: In this paper, the Fokker-Planck equation for the neutron density probability distribution in a multiplying system, possessing random source and random parametric excitation, is deduced.
01 Jan 1969
TL;DR: In this paper, the authors discuss approximate continuous nonlinear minimal-variance filtering, which is a form of sequential stochastic estimation and has its roots in the early least-squares differential correction schemes for orbit determination.
Abstract: Publisher Summary This chapter discusses approximate continuous nonlinear minimal-variance filtering. Continuous minimal-variance filtering is a form of sequential stochastic estimation and, as such, has its roots in the early least-squares differential correction schemes for orbit determination. The feature common to the early filtering studies is the derivation of an integral equation for the optimal filter. In the special case of linear filtering for stationary statistics, the integral equation can be solved in a useful form for many applications; unfortunately, the same cannot be said for the more general cases. The true nonlinear minimal-variance filter states that the fundamental entity in sequential estimation is the conditional probability density function of the message process given the measurement process. If the density is known as a function of time, so is the minimal-variance estimate. A white noise is a random process with a power spectral density which is a constant, or, equivalently, an autocorrelation function, which is a Dirac δ-function. Such a process has no physical meaning as it would require infinite signal power. The foregoing definition is valid for stationary white noise, though the autocorrelation-function definition can be extended to the nonstationary case by allowing a time-varying coefficient for the δ-function.
01 Jun 1969
TL;DR: In this paper, it was shown that a probability distribution governing the fluctuation of the intensity of random noise containing some periodic or aperiodic signal wave can be well approximated by the noncentral χ2distribution and also that further approximation leads to the logarithmico-normal distribution.
Abstract: It is shown that a probability distribution governing the fluctuation of the intensity of random noise containing some periodic or aperiodic signal wave can be well approximated by the noncentral χ2distribution and also that further approximation leads to the logarithmico-normal distribution which is simpler and more convenient in practical applications.
TL;DR: In this paper, special silicon MOS transistors are fabricated to demonstrate that the proposed "excess white noise" attributed to the mobility fluctuation does not exist, and the previously observed excess noise over the white thermal noise is shown to be caused by a 1/f-type noise component due to noise measurements at insufficiently high frequencies on devices which have very high 1 /f noise.
Abstract: Special silicon MOS transistors are fabricated to demonstrate that the proposed ‘excess white noise’ attributed to the mobility fluctuation does not exist. The previously observed excess noise over the white thermal noise is shown to be caused by a 1/f-type noise component due to noise measurements at insufficiently high frequencies on devices which have very high 1/f noise.
Patent•
29 Jan 1969
TL;DR: In this paper, a modulator for down modulating the carrier frequency of the received sonar pulse and delay devices for delaying the pulse by varying degrees equivalent to the travel times for the pulse between successive major echo producing discontinuities in the target whose echo is being simulated to form a series of pulses.
Abstract: Apparatus for simulating acoustic echoes of sonar pulses from any selected target configuration including a hydrophone whose output signal is fed to a signal processor for modifying a received sonar pulse and generating an electrical echo analogue signal applied to a projector for transmission. The processor includes a modulator for down modulating the carrier frequency of the received pulse and delay devices for delaying the pulse by varying degrees equivalent to the travel times for the pulse between successive major echo producing discontinuities in the target whose echo is being simulated to form a series of pulses. The pulses are controlled in amplitude in accordance with the appropriate target strengths for the succession of discontinuities and are fed to fill-in and summing circuits for adding white noise of desired envelope characteristics in the intervals between successive pulses to form the echo analogue signal. A second modulator shifts the frequency band of the echo analogue signal upwardly and introduces a selected Doppler shift thereinto prior to its application to the projector for acoustic transmission. Feedback elimination circuitry delays and shifts the phase of the echo analogue signal and applies the resulting signal to a summer for eliminating the effect of acoustic feedback.
01 Feb 1969
TL;DR: The method is called "MECHANICAL FREQUENCY MODULATION of MFM" because it combines the MATHEMATICS ASSOCIATED with ASSOCIAL "FREQUENCYMODULATION" Theory with the theory of "white noise".
Abstract: THIS PAPER USES SNOW TIRE TREAD NOISE TO DEMONSTRATE A MATHEMATICAL WAY FOR COMPUTING AN UNEVEN SPACING SO THAT THE EXCITATION OR NOISE SOURCE IS IN THE PREFERRED FORM FOR WHINE REDUCTION-"WHITE NOISE." THE METHOD USES THE MATHEMATICS ASSOCIATED WITH ASSOCICAL "FREQUENCY MODULATION" THEORY AND, THEREFORE, IS CALLED "MECHANICAL FREQUENCY MODULATION" OF MFM. /AUTHOR/
TL;DR: In this paper, a model of the form of a linear time-invariant difference equation with a stationary independent random sequence driving function is proposed and investigated, and the problem of estimating the a priori statistics of a nonstationary process is considered using finite-time averages of experimental data.
Abstract: The problem of estimating the a priori statistics of a nonstationary process is considered using finite-time averages of experimental data. A model of the form of a linear time-invariant difference equation with a stationary independent random sequence driving function is proposed and investigated. Finite-time averages are calculated and then used in a steepest descent method to determine the coefficients of the difference nce equation. Methods are presented for transforming this model to the statespace pace format necessary for Kalman filtering, and an example is given using actual gyro drift-rate data.
TL;DR: Differential equations for minimum variance linear filter separating signals from additive correlated noise, using discrete time optimum formulas, are presented in this paper. But they do not consider the effect of correlated noise.
Abstract: Differential equations for minimum variance linear filter separating signals from additive correlated noise, using discrete time optimum formulas