AN EXTENSION OF THE KAC-SIEGERT RESULTS AND RELATED TOPICS.

Abstract

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)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1967
Accession Number
AD0662660

Entities

People

  • Robert D. Turner

Organizations

  • Institute for Defense Analyses

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Bandwidth
  • Coefficients
  • Distribution Functions
  • Integrators
  • Mathematics
  • Probability
  • Probability Distributions
  • Signal Processing
  • Standards

Readers

  • Electronics Engineering
  • Statistical inference.