Showing papers on "White noise published in 1973"

Characterization of Frequency Stability: Uncertainty due to the Finite Number of Measurements

Abstract: We consider the characterization of the frequency stability of signal generators by means of the Allan variance of their fractional frequency fluctuations. As the number m of measurements is always finite, one can only get an estimate of this variance, which is a random function of m. We calculate the variance of the Allan variance for commonly encountered spectral densities of frequency fluctuations and deduce the relative uncertainty in the evaluation of frequency stability, as a function of m. The theory is experimentally checked for white noise of phase and flicker noise of frequency. The main hypothesis of the calculations, i.e., the Gaussian character of frequency fluctuations is verified. The m dependence of the uncertainty (one sigma) in the evaluation of frequency stability agrees with the predicted value.

Minimal structural response under random excitation using the vibration absorber

Abstract: The equations of motion are derived for the first mode response of a linear multistorey structure having a linear vibration absorber attached to the roof. Furthermore, the variance of the first mode response to a gaussian white noise lateral base acceleration (as a model of earthquake excitation) is determined. Smallest possible values of the variance of the response along with corresponding absorber parameters are established using an optimization program. It is demonstrated that the absorber is quite effective in reducing first mode response for 5- and 10-storey structures even with relatively small values of the absorber mass. Moreover, minimal responses for the randomly excited single-degree-of-freedom system have been determined, and a design example is presented. The absorber system has potential application not only in earthquake engineering but also in aerospace and terrestrial vehicle design.

Development and application of white-noise modeling techniques for studies of insect visual nervous system.

Abstract: The nonlinear system identification technique through white-noise stimulation is extended to multi-input, -output systems with consideration given to applications in the functional study of the nervous system. The applicability of the method is discussed in general and in particular for the motion detection neuronal system of the fly. Two series of experiments are performed; one with moving striped-pattern stimuli and the other with spot stimuli of fluctuating intensity. In both cases nonlinear dynamic models are derived which describe the system with considerable accuracy over the frequency range of 0.2–50 Hz and a dynamic amplitude range of about 40-1. These models are able to predict accurately all the discrete experiments so far performed on this system for which the models are applicable. The differences in dynamic characteristics between the corresponding system of the Musca and Phoenicia families of flies are minor except for a difference in latencies and if the difference in geometry of their faceted eyes is taken into account. The large field response of the motion detection unit is a linear weighted summation of all the smaller field highly nonlinear subsystems of which the large field is comprised.

Plane waves at small arrays

Abstract: The resolving power of a seismic array is defined in terms of the array response function and via the classical uncertainty principle. Using the theory of maximum likelihood wavenumber spectra (Capon, 1969), we show for the case of two correlated plane waves that arbitrarily high resolution is achievable in the limit as the background white noise tends to zero. This extends Barnard’s (1969) result to the case of correlated plane waves. The increased resolution arises from the additional assumption that the data are plane waves over all space, and not zero off the array as the classical result assumes. It is found that a sample rate (in time) large compared to the Nyquist rate, is needed in the case of a short time gate at a small array. Cross‐power spectral matrices are estimated at 4 hz from 1 sec of computer generated data consisting of two correlated plane waves in white noise. These spectral matrices are then used to generate maximum likelihood wavenumber spectra. The two plane waves are resolved at v...

Mean square stability criteria for stochastic feedback systems

Abstract: In this paper several stability criteria are obtained for a class of stochastic feedback systems containing a multiplicative white noise element ; continuous time as well as discrete time systems are dealt with. Mean square stability properties are derived by means of Lyapunov theory ; the Lyapunov functions are generated by means of the Lyapunov equation, the path integral technique, and the Kalman-Yacoboviteh lemma. Results similar to the Routh-Hurtwitz conditions and the circle criteria for deterministic feedback systems are discussed. Different interpretations of the white noise element (Ito, Stratonovitch, etc.) are considered.

Kalman filtering with no A-priori information about noise-White noise case: Part I: Identification of covariances

Abstract: Kalman filtering in the presence of white process and measurement noises having unknown means and covariances is considered. Only stationary linear discrete stochastic systems are considered. It is shown that the identification of noise covariances can be done without the knowledge of noise means. This means that the problem of identifying the noise statistics can be decomposed into two separate subproblems, namely, 1) identification of noise covariances and 2) identification of noise means, and that these two subproblems can be solved in that order. A procedure for identifying noise covariances is developed in this paper. It is a nontrivial extension of Mehra's results to the case where the process and measurement noises have unknown means, and are correlated with each other. This procedure, like Mehra's, can be used either in a nonrecursive mode, or in a batch-recursive mode. Solution of subproblem 2), and the standard Kalman filter algorithm are not discussed since they are well known in the literature.

Masking of auditory responses in the medulla oblongata of goldfish.

Abstract: 1. The nervous activity of single auditory neurones in goldfish brain have been measured. 2. Four types of acoustic stimuli were used, (1) pure tones, (2) noise of one-third octave band width, (3) noise of one-octave band width with centre frequency equal to the pure tone, and (4) white noise. 3. Except for white noise, these stimuli produced the same response to equal sound pressures. The white noise response was less, presumably because the frequency range covered by a single neurone is far narrower than the range of white noise. 4. The conclusion has been reached that for low-frequency acoustic signals, the acoustic power over a frequency band of one to two octaves is integrated by the nervous system. 5. The masking effect of background noise on the acoustic threshold of single units to pure tones is strongest when the noise band has the same centre frequency as the test tone. In this case the tone threshold increases linearly with the background noise level. 6. When the noise band was centred at a different frequency from the tone, the masking effect decreased at a rate of 20-22 dB/octave for the first one-third octave for a tone frequency of 250 Hz. For a tone of 500 Hz the masking effect of lower frequencies was stronger and was reduced by only some 9 dB/octave for the first one-third octave.

On the identifiability of linear dynamical systems

Abstract: Consider the situation in which the unknown parameters of a stationary linear system may be parametrized by a set of unknown parameters. The question thus arises of when such a set of parameters can be uniquely identified on the basis of observed data. This problem is considered here both in the case of input and output observations and in the case of output observations in the presence of a white noise input. Conditions for local identifiability are derived for both situations and a sufficient condition for global identifiability is given for the former situation, i.e., when simultaneous input and output observations are available.

Method and apparatus for detecting and quantifying cardiovascular murmurs and the like

Abstract: A system for extracting information concerning a defect manifested by random noise from a composite signal that includes a periodic portion and a random noise portion. The composite signal is formed into a series of time records by employing some trigger signal that identifies the beginning of the periodic signal. A series of the time records is summed to average out the random noise portion and produce a signal containing only the periodic, synchronous, signal portion. Concurrently, the composite signal time records are squared to retain the random portion as well as the synchronous portion and the same series of squared time records is summed. Subtraction of the square of the former summed signal from the latter eliminates the synchronous portion so as to produce a time record which, after being scaled by a factor 1/N, for N time records, is a measure of the power of the random noise signal. Analysis of the random noise power signal permits appraisal of the condition creating the noise signal.

Rotor Blade Response to Random Loads: A Direct Time-Domain Approach

Abstract: The response of a rotor blade subject to random loads is treated within the framework of time-varying linear dynamical systems with nonstationary random forcing functions. The statistically meaningful characteristics of the response, namely the covariance and the correlation, are directly obtained from a pair of ordinary matrix differential equations in the time domain. Extensive results for different models of a rigidly flapping blade subject to quasi-stationary random excitations have been obtained by this direct time-domain approach to demonstrate its simplicity and efficiency.

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.

On the error matrix in optimal linear filtering of stationary processes

Abstract: The error covariance matrix corresponding to optimal linear causal filtering of second-order stationary processes in additive noise is considered. Formulas expressing this error matrix in terms of the optimal transfer function are established, and in the nonsingular case the optimal transfer function is expressed in terms of the spectral densities. These are straightforward generalizations of previously published scalar results, and the derivation is similarly based on Hardy space theory. Explicit bounds on the minimal error (i.e., the trace of the optimal error covariance matrix) are obtained for filtering in white noise. Furthermore, an explicit expression for the error covariance matrix is derived for the case of transmitting the same signal over several white-noise channels.

The treatment of bias in the square-root information filter/smoother

Abstract: The Dyer-McReynolds square root information filter (SRIF) is rederived, using recursive least squares arguments. The result is applied to a system composed partly of biases. The filter "sensitivity" matrix, "computed" covariance, and "consider" covariance for this augmented system are reviewed. A new computationally attractive representation for the smoothed estimates, in terms of a smoothed "sensitivity" matrix and a smoothed "computed" covariance is presented.

Transient Characteristics of Simple Systems to Modulated Random Noise

Abstract: Discussed are the mean-square response exceedance characteristics of a single-tuned system to amplitude modulated noise. The results bear on the accuracy of spectral estimates of nonstationary data, and subsequently, relate directly to the design, analysis, and testing of structural systems in environments as gusts, earthquakes, and ignition transients. For noise correlated as an exponentially damped cosine, the nonstationary response may exceed its stationary value by a factor in excess of two. A time-varying shaping filter explanation is offered for this behavior. For white noise, such exceedances do not occur.

Doppler signal simulator

Abstract: A doppler signal simulator in which a composite doppler spectra including background noise, signal, leakage signal, and image beam signals simulating, in proper sequence, each of the four beams of a doppler navigation system is shown. White noise is generated digitally to provide background noise, and to obtain the doppler return spectra by filtering with digital commutating filters controlled by a plurality of center frequencies generated by logic circuits. Leakage and image signals are generated and added to the doppler spectra and noise to provide the four composite signals which are then multiplexed and filtered to provide the final output. Gain control is provided for the various signals to simulate various flight conditions. Selection logic allows selecting a signal to test the post IF and tracker or tracker alone. All controls are adaptable to digital control so that comprehensive testing under control of a digital computer is possible.

On the distribution and moments of RC -filtered hard-limited RC -filtered white noise

Abstract: Suppose white noise is put into an RC filter with time constant 1/a whose output is hard limited and fed into a second RC filter with time constant 1/b . The density of the output y(t) of the system has been the subject of several investigations. Most recently, Pawula and Tsai made the conjecture that for Gaussian white noise the y(t) density is given by a certain expression, a special case of which was derived earlier by Doyle, McFadden, and Marx for b/a = 2 . In this paper an expression for the n th moment of y(t) is found. From the expression for the fourth moment, it is proven that the Pawula-Tsai conjecture is not true in general. It is further found that if the output of the hard limiter were wide-sense Markov, the Pawula-Tsai conjecture would be true.

Estimation of Uncertain Systems

Abstract: Publisher Summary This chapter describes the state estimation problem with parameter uncertainties. The Kalman-Bucy filter gives the unbiased, minimum variance estimate of the state vector of a linear dynamic system that is disturbed by additive white noise when measurements of the state vector are linear, but disturbed by white noise. Such performance is not realized in actual practice because the information that is required to construct the Kalman-Bucy filter is approximately known. The noise parameters and models might be based upon few data points, computer round-off errors might be significant, and the system model might not be adequate. When it is impractical or impossible to arrive at accurate information upon which to base the filter design, suboptimal and adaptive techniques must be considered. The chapter discusses a technique that has been established to allow Kalman-Bucy filtering in an uncertain environment when the complexity of the estimation algorithm is constrained. The problem of the establishment of a method of Kalman-Bucy filter design, when the noise covariance matrices and the state matrix are uncertain, but bounded with known bounds has been presented in the chapter.

Transient Random Response of Bilinear Oscillators

Abstract: Results of an empirical study of the transient mean-square response of bilinear hysteretic oscillators to random excitation are presented. The oscillators considered include a moderately nonlinear system, a nearly elasto-plastic system, and the truly elasto-plastic system. The random excitation considered is an approximate simulation of stationary, Gaussian white noise. Generation of the ensemble of time histories of excitation, and integration of the nonlinear equation of motion to obtain the ensemble of time histories of response were performed on a digital computer. It is found that a constant parameter linear system (such as the Krylov-Bogoliubov system) can give acceptable predictions of the transient mean square response of a moderately nonlinear system, but not of a nearly elasto plastic system. A variable coefficient linear system which does give acceptable response predictions for the nearly elastoplastic system is also presented.

An all digital phase locked loop for synchronization of a sinusoidal signal embedded in white Gaussian noise

Abstract: An all digital phase locked loop which tracks the phase of the incoming sinusoidal signal once per carrier cycle is proposed. The different elements and their functions and the phase lock operation are explained in detail. The nonlinear difference equations which govern the operation of the digital loop when the incoming signal is embedded in white Gaussian noise are derived, and a suitable model is specified. The performance of the digital loop is considered for the synchronization of a sinusoidal signal. For this, the noise term is suitably modelled which allows specification of the output probabilities for the two level quantizer in the loop at any given phase error. The loop filter considered increases the probability of proper phase correction. The phase error states in modulo two-pi forms a finite state Markov chain which enables the calculation of steady state probabilities, RMS phase error, transient response and mean time for cycle skipping.