Showing papers on "White noise published in 1975"

A case where interference does not reduce capacity (Corresp.)

Abstract: It is shown that, under certain conditions, two strongly interfering communication links with additive white Gaussian noise can achieve rates as high as would be achievable without this interference.

Persistence of Dynamical Systems under Random Perturbations

Abstract: Random perturbations may decisively affect the long-term behavior of dynamical systems. Random effects are modeled by the addition of Gaussian white noise to the system. The resulting diffusion equ...

Application of Optimal Control Theory to Civil Engineering Structures

Abstract: Modern control theory has been successfully applied to control the motions of aerospace vehicles. An exploratory study is made herein to investigate the feasibility of applying such a theory to control the vibration of civil engineering structures under random loadings. It is assumed that random excitations to structures, such as wind loads and earthquakes, can be modeled by passing either a stationary Gaussian white noise or a nonstationary Gaussian shot noise through a filter. The performance index to be minimized consists of the covariances of both the structural responses and the control forces. Under these conditions, the optimal control law is a linear feedback control. The optimal control forces are obtained by solving a matrix Riccati equation. Applications of the optimal control to a multi-degree-of-freedom structure, under stationary wind loads and nonstationary earthquakes, are demonstrated. It is shown that significant reduction in covariances of the structural responses can be achieved by the use of an active control system.

A comparison of power spectral estimates and applications of the maximum entropy method

Abstract: A new spectral estimate, called the maximum entropy method, is described. This estimate was originated by John Parker Burg for use in seismic wave analysis. In the maximum entropy method the entropy, or information, of a signal is maximized under the constraint that the estimated autocorrelation function of the signal is the Fourier transform of the spectral power density. The spectral estimates are calculated in two ways: (1) by minimization of the error power to obtain the coefficients of the prediction error filter, as suggested by Burg, and (2) by a direct solution of the matrix equation using an algorithm due to Norman Levinson. For comparison a Blackman-Tukey technique, calculated with a Hamming window, is used also. We illustrate these three methods by applying them to a composite signal consisting of four sinusoids of unit amplitude: one each at high and low frequencies and two at moderate frequencies with respect to the Nyquist frequency, to which is added white noise of 0.5 amplitude. Results are shown to indicate that the best correspondence with the input spectrum is provided by the Burg technique. Applications of the maximum entropy method to geomagnetic micropulsations reveal complex multiplet structure in the Pc 4, 5 range. Such structure, not previously resolved by conventional techniques, has been predicted by a recent theory of magnetospheric resonances. In a period range 7 orders of magnitude longer than micropulsation periods, analysis of annual sunspot means shows that the 11-yr band is composed of at least three distinct lines. With each of these lines is associated a harmonic sequence. Long periods of the order of 100 yr also are revealed.

More on autoregressive model fitting with noisy data by Akaike's information criterion (Corresp.)

Abstract: Davisson [131, [141 has considered the problem of determining the "order" of the signal from noisy data. Although interesting theoretically, his result is difficult to use in practice. In this correspondence, we exploit one well-known fact concerning autoregressive (AR) signals plus white noise, and using Akaike's information criterion [15], [17], we have developed one efficient procedure for determining the order of the AR signal from noisy data. The procedure is illustrated numerically using both artificially generated and real data. The connection between the preceding problem and the classical statistical problem of factor analysis is discussed.

Autoregressive Representation of Seismic P-wave Signals with an Application to the Problem of Short-Period Discriminants

Abstract: Summary It is shown that seismic P-wave signals can be represented by parametric models of autoregressive type. These are models having the form X(t)-a1X(t–1)-…- apX(t-p) =Z(t) where X(t) is the digitized short-period data time series defined by the P-wave signal, and Z(t) is a white noise series. The autoregressive analysis is undertaken for 40 underground nuclear explosions and 45 earthquakes from Eurasia. For each event a separate analysis of the noise preceding the event as well as of the P-wave coda has been included. It is found that in most cases a reasonable statistical fit is obtained using a low order autoregressive model. The autoregressive parameters characterize the power spectrum (equivalently, the autocorrelation function) of the P-wave signal and form a convenient basis for studying the possibilities of short-period discrimination between nuclear explosions and earthquakes. A preliminary discussion of these possibilities is included.

Quantization errors in the fast Fourier transform

Abstract: When a fast Fourier transform (FFT) is implemented on a digital machine, quantization errors will arise due to finite word lengths in the digital system. The magnitudes and characteristics of these errors must be known if an FFT is to be designed with the minimum word lengths needed for acceptable performance. Two forms of FFT quantization, coefficient rounding and floating point arithmetic quantization, are analyzed in this paper. A theory is presented from which several new results can be obtained. The error characteristics of FFT's using exact and truncated values for the coefficients 1 and -j are found to be roughly equivalent. The accuracy of the theory is tested by computer simulations. Using the models introduced in this paper, new and accurate models can be derived to model quantization errors in high-speed convolution filters.

Responses of single units in the cochlear nucleus of the cat to cosine noise.

Abstract: The response of single cells in the cochlear nucleus of the cat to noise with a cosinusoidal power spectrum (cosine noise) was studied. Cosine noise is obtained by adding white noise to the same noise delayed over a time τ; maxima in the spectrum occur at n/τ (n=0,1,2,⋅⋅⋅). The spike rate of a unit was continuously registered as a function of τ (τ diagram). This registration shows a periodic fluctuation having maxima at τ=n/CF and troughs at τ= (n+1/2)/CF, with a decreasing peak–trough ratio for increasing n (CF is the characteristic frequency of the unit). For the majority of the units investigated, a maximal peak–trough ratio was observed not for n=0 but for about n=3. This is ascribed to lateral inhibition. By introducing the mathematical concept of a weighting function in the frequency domain, a quantitative relation with the response of the unit to a pure tone in white noise (iso‐intensity curve) could be established. The results are compared with psychophysical results on the internal representation...

Acoustic Emission in the Frequency Domain

Abstract: A means for quickly and easily determining the broadband frequency content of acoustic bursts as short as 20 μs in duration has been developed using a video tape recorder and a standard spectrum analyzer. It is shown by examples from several tests on laboratory specimens and on large structures that the frequency content of an acoustic burst is related to the mechanism which produced it and is not affected substantially by the specimen size or by mode conversion due to multiple reflections in the structure. The frequency content of the burst can be changed in two ways, however: by the frequency-dependent attenuation of the propagation medium and in the cases where the medium is dispersive. Results of measurements on the effect of these factors in a variety of structures are given. Although acoustic emissions from many materials tend to be "white noise," several examples of acoustic emissions and exwaneous background noise bursts having distinctive frequency spectra are given which suggest possibilities for discriminating true acoustic emission signals from background noise on the basis of frequency content alone.

Impulsive Noise in Noncoherent M-ary Digital Systems

Abstract: This concise paper analyses the performance of noncoherent M -ary digital systems in presence of a generalized stationary Poisson impulsive noise process, with a receiver operating as a maximum likelihood detector in white Gaussian interference. Methods to bound the error probability for ASK, PSK, and FSK systems in the cases where the noise is impulsive and quasi-Gaussian are described and the results discussed.

Filtering for Systems Excited by Poisson White Noise

Abstract: The application of martingale theory to filtering problems for linear systems, excited by Poisson white noise but with Gaussian observation noise, is described. Stochastic differential equations for the conditional density function and moments are derived, and two approximate methods for solving these equations are developed. Numerical results are presented. Preliminary results are given for the smoothing problem, and for filtering problems for distributed parameter systems excited by Poisson white noise.

On the stochastic stability of linear systems containing colored multiplicative noise

Abstract: The stability of linear systems containing colored multiplicative or state-dependent noise processes is considered. We present a technique for obtaining necessary and sufficient conditions for the p th moment stability of linear systems satisfying certain Lie-algebraic conditions. An example is given to illustrate the technique.

The Influence of Noise on Stutterers' Different Disfluency Types

Abstract: The purpose of this study was to determine the effects of noise on the types of disfluencies of stutterers. Seventeen adult stutterers read prose aloud in the presence of a white noise (95 dB SPL)....

Fourier analysis of random sequences

Abstract: Computer-generated random sequences were submitted to a Fourier analysis. The distribution of the phase angle was not uniform over the circle, but some “bald patches” remained. The Fourier analysis itself allows the construction of ideal random sequences. For an “ideal white noise” the amplitudes were chosen as one, whereas the phase angles were uniformly distributed. For an “ideal random noise” both phase angles and amplitudes were uniformly distributed. Thus, ideal noise patterns were obtained which were analysed statistically.

Optimization of structures undergoing harmonic or stochastic excitation

Abstract: The optimal design was investigated of simple structures subjected to dynamic loads, with constraints on the structures' responses. Optimal designs were examined for one dimensional structures excited by harmonically oscillating loads, similar structures excited by white noise, and a wing in the presence of continuous atmospheric turbulence. The first has constraints on the maximum allowable stress while the last two place bounds on the probability of failure of the structure. Approximations were made to replace the time parameter with a frequency parameter. For the first problem, this involved the steady state response, and in the remaining cases, power spectral techniques were employed to find the root mean square values of the responses. Optimal solutions were found by using computer algorithms which combined finite elements methods with optimization techniques based on mathematical programming. It was found that the inertial loads for these dynamic problems result in optimal structures that are radically different from those obtained for structures loaded statically by forces of comparable magnitude.

Relationships between identifiability and input selection

Abstract: This paper points out a relationship between identifiability and input selection for multiparameter systems. Two examples are given to illustrate this relationship.

Probability of First-Passage Failure for Nonstationary Random Vibration

Abstract: For systems responding to stationary random excitation, the problem of calculating the probability, P(T), that first passage failure occurs within an interval of time, Of . is considered. By an analysis based on the "in and exclusion" series it is shown that, under certain conditions, P(T) tends to a simple exponential form, as T becomes large. A series expression for the limiting decay rate is deduced. It is demonstrated that the first three terms in the series can be evaluated if the response process is normally distributed, and various methods of estimating the limiting decay rate from these terms are given. In the case of a linear oscillator excited by white noise, numerical results are displayed for a range of critical barrier heights and damping factors, and the analytical estimates of the limiting decay rate are compared with corresponding digital simulation estimates. OR systems responding to random excitation it is important to predict the probability that failure will occur, within a specified time interval. This requires the formulation of a suitable failure criterion. In this paper it will be assumed that failure occurs when the amplitude of the random vibration first exceeds some critical level. This "first-passage" type of failure is of considerable practical importance, since it corresponds to many physical failure mechanisms. The problem of predicting the probability P(T) that firstpassage failure will occur within an interval 0-T is a classical one, of severe analytical difficulty. An exact theoretical solution, in closed form, has not yet been found but recently many approximate solutions have been devised which, together with simulation results, have revealed the essential character of the solution. Crandall has recently compared a number of these approximations.1 Further approximate theoretical approaches are described in Refs. 2-7. In this paper attention is focussed on the case where the random vibration is stationary and the mean time to failure is very long compared with the natural period of oscillation of the vibrating system. Clearly, long times to failure are associated with high critical amplitude levels and hence are of most concern in practical applications. Despite the importance of this particular case, comparatively little attention has been given in the literature to the limiting form of P(T), when T is large. A notable exception is the work of Crandall et al. 8 who found that, for a linear oscillator responding to white noise excitation, the distribution of the first passage time tends towards a simple exponential form, as T becomes large. Mark9 has conjectured that this limiting form can be expected in any situation where the random vibration is stationary. Here the limiting form of P(T) for large T is examined in some detail, by an analysis based on the "in and exclusion" series.10 In an earlier paper11 it was shown that this series can be used to generate a sequence of upper and lower bounds to P(T). Numerical results for a linear oscillator showed that these bounds tend to diverge as T increases. It would appear, therefore, that the series solution can yield little or no information on the behavior of P(T) for large T. However, in a paper of outstanding importance,12 Kuznetsov et al. have shown that by a suitable transformation of the in and exclusion series it is possible to deduce the limiting form of P(T) for

Random pulse generator

Abstract: An exemplary embodiment of the present invention provides a source of random width and random spaced rectangular voltage pulses whose mean or average frequency of operation is controllable within prescribed limits of about 10 hertz to 1 megahertz. A pair of thin-film metal resistors are used to provide a differential white noise voltage pulse source. Pulse shaping and amplification circuitry provide relatively short duration pulses of constant amplitude which are applied to anti-bounce logic circuitry to prevent ringing effects. The pulse outputs from the anti-bounce circuits are then used to control two one-shot multivibrators whose output comprises the random length and random spaced rectangular pulses. Means are provided for monitoring, calibrating and evaluating the relative randomness of the generator.

"Design of Experiments" for the Identification of Linear Dynamic Systems

Abstract: One of the most important problems in direct digital controller design is to determine the process model from the sampled data. Goodness of the control depends considerably on the accuracy of the identified model. This paper investigates how to generate optimal input signal series for the identification of linear discrete-time systems in order to improve the accuracy of estimates. The determinant of the covariance matrix or of the inverse of the information matrix is considered as a measure of the error in the parameter estimates. Very simple methods are presented for the minimization of these criteria in case of an amplitude constrained input signal.

Analog-to-digital converter utilizing a random noise source

Abstract: An analog-to-digital converter arranged to accept an analog input signal and to convert it into an output having digital form The converter is characterized by a reference random noise source which generates random noise signals with uniform amplitude occurrence probability density in a given range, and by an amplitude comparator arranged to repeatedly compare the amplitude of the random noise signal with the amplitude of a signal varying with the analog signal to be converted The amplitude comparator supplies output pulses in accordance with the comparisons, eg, whenever the analog signal amplitude is greater than the random noise amplitude, and the number of pulses from the amplitude comparator in a measurement interval then digitally corresponds to the value of the analog signal and may be utilized, as in a display Resolution of the converter is increased beyond the minimum amplitude increment of the random noise source signal in one embodiment by superposition on either the analog signal or the random noise signal of a triangular wave with an amplitude greater than the minimum amplitude increment of the random noise signal, and in another embodiment by superposition of a second random noise signal

Stability criteria for discrete-time systems with colored multiplicative noise

Abstract: Often a mathematical model of a dynamical system requires the consideration of uncertain elements. Historically, emphasis has been placed on studying systems in which disturbances enter additively, but many control problems include disturbances that can be more naturally modeled as uncertain (time-varying) multiplicative gains. If the multiplicative gain is of the white noise type, necessary and sufficient conditions for the stability of many of these systems have been derived previously. In this article, we develop conditions for the stability of some discrete-time systems containing multiplicative colored noise. Discrete-time systems in which the colored noise is generated nonrecursively are studied. Necessary and sufficient conditions for their mean square stability have been obtained, and numerical solutions are provided for cases in which the colored noise parameter is generated recursively.

Low SNR Digital Communication over Certain Additive Non-Gaussian Channels

Abstract: This paper presents a simple formula for the capacity of a coherent digital communication channel operating near threshold [i.e., with very low signal-to-noise ratio (SNR)] with additive noise from a certain class of arbitrary but known probability distributions. For the noncoherent threshold channel, the optimun receiver is derived for arbitrary modulations and fading. This receiver is shown to specialize to previously derived canonical froms for unmodulated signals.