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# Accession Number:

## AD0711112

# Title:

## STATISTICAL THEORY FOR THE DETECTION OF SIGNALS UNDER LINEAR SCALE TRANSFORMATIONS.

# Descriptive Note:

## Doctoral thesis,

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS

# Report Date:

## 1970-04-20

# Pagination or Media Count:

##
53.0

# Abstract:

## Most of the literature of signal detection assumes a parametric signal model of the form ft beta St - t sub O where the amplitude beta and the time of arrival t sub 0 are unknown. Many of the questions remain unanswered about signals of the form beta Sat - t sub 0 where a is an unknown scale parameter. Several basic results are presented about the reception of signals of this more general form. The likelihood Ratio Test for detection is developed and curves of probability of detection as a function of signal-to-noise ratio are given for various false alarm rates. Detection in the case of multiple observations is also considered. Estimation of the unknown signal parameters beta, a, t sub O and the unknown noise variance Sigma squared is treated. The maximum likelihood or least squares estimators for these parameters are given, along with an iterative computational technique. The large sample distribution of the estimators is also given. Two types of signal classification problems are discussed and the Bayes decision rules for their solutions are presented. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#