AN EXTENSION OF THE KAC-SIEGERT RESULTS AND RELATED TOPICS.
INSTITUTE FOR DEFENSE ANALYSES ARLINGTON VA SCIENCE AND TECHNOLOGY DIV
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A tractable expression for the probability distribution of the output of a signal-processing configuration analyzed by Kac and Siegert is derived. The configuration consists of a single-tuned narrow-band input stage, followed by a square-law device, followed by a simple RC integrator. The expression obtained is useful for arbitrary values of the input-output bandwidth ratio. Expressions for the coefficients and parameters of a seven-term Edgeworth series approximation to the probability distribution of a more general configuration are presented for the zero-signal case, and for a two-term approximation when an arbitrary signal is present. The extended Kac-Siegert result is then employed to check the accuracy of the zero-signal Edgeworth approximation for an input-output bandwidth ratio of 50. It is found that the approximation is accurate out to about 4.3 standard deviations beyond the mean, corresponding to a probability of 0.0005 of exceeding the distribution function variable. Author