Estimation of the Average Frequency of a Random Process
CHICAGO UNIV IL LAB FOR ATMOSPHERIC PROBING
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The purpose of the report is to develop a means of estimating, in real time, the average frequency of a random process, given only a time-limited sample of that process. The average frequency of a random process is defined in terms of the power spectral density. Previous estimators of average frequency were mathematically based on estimating the power spectral density. In this work, the average frequency is expressed in terms of the autocorrelation and cross-correlation functions, and a new estimator is obtained which is based on estimates of these correlation functions. Two estimators presented in the literature and the proposed estimator are compared, and expressions are obtained for the power spectral density and autocorrelation function at each point in the systems, exclusive of the outputs. Approximate expressions are obtained for the bias and variance of the proposed estimator and one of the referenced estimators. A lab model of the proposed device was constructed and tested under several sets of operating conditions. It is found that, under typical operating conditions, the proposed estimator performs almost as well as those proposed earlier, and is simpler in form. For very short samples of the random process, however, the difference in variance becomes more noticeable.
- Statistics and Probability