Browsing by Author "Barnett, John T."
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Item Power Considerations in Acoustic Emission(1995) Barnett, John T.; Clough, Roger B.; Kedem, Benjamin; ISRIn stochastic acoustic emission, both theory and experiments suggest that the power of the acoustic emission signal is proportional to the source energy. Hence, inference about the power is equivalent to inference about the source energy except for a constant multiple. In this regard, the connection between peaks exceeding a fixed level and the power in random acoustic emission waves is explored when the source energy is an impulse of short duration. Under certain conditions, the peak distribution is sensitive to power changes, determines it and is determined by it. The maximum likelihood estimator of the power from a random sample of peaks- the peak estimator - is more efficient than the maximum likelihood estimator - average sum of squares - from a random sample of the same size of signal values. When evaluated from nonrandom samples, indications are that the peak estimator may still have a relatively small mean square error. A real data example indicates that the left-truncated Rayleigh probability distribution may serve as an adequate model for high peaks.Item Zero-Crossing Rates of Some Non-Gaussian Processes with Application to Detection and Estimation(1996) Barnett, John T.; Kedem, B.; ISRIn this dissertation we present extensions of Rice's formula for the expected zero-crossing rate of a Gaussian process to some useful non-Gaussian cases. In particular, we extend Rice's formula to the class of stationary processes which are a monotone transformation of a Gaussian process, to countable mixtures of Gaussians, and to products of independent Gaussian processes. In all the above mentioned cases the expected zero-crossing rates are given for both continuous time and discrete time processes. We also investigate the application of parametric filtering, using zero-crossing count statistics, to the problem of frequency estimation in a mixed spectrum model and the application of mean- level-crossing counts of the envelope of a Gaussian process to a radar detection problem. For the radar problem we prove asymptotic normality of the level-crossings of the envelope of a Gaussian process and provide and expression for the asymptotic variance.