Accession Number:

AD0603710

Title:

LIMITING FORMS AND NON-GAUSSIAN STATISTICS IN SIGNAL PROCESSING THEORY, I.

Descriptive Note:

Technical rept.,

Corporate Author:

LITTON SYSTEMS INC WALTHAM MASS

Personal Author(s):

Report Date:

1964-04-15

Pagination or Media Count:

52.0

Abstract:

This report presents an introductory study of representations of non-normal processes and their approach to normality under special conditions. In particular, the Edgeworth series development is applied, in one and more dimensions, to obtain conditions for a process to exhibit gaussian structure, whether under discrete or continuous sampling on an interval. For the former, the usual condition is that of a large number of independent samples essentially, the critical condition required in the central limit Theorem, such that the Edgeworth correction terms vanish through all orders. It is shown, also, that this condition may not obtain for certain types of process, where an alternative Laguerre development may be more appropriate, characterized by a form of chi square - distribution with few degrees of freedom. Some processes that are inherently non-gaussian, such as the important Poisson process an example of an infinitely divisible point-process, become essentially normal when their point-density becomes sufficiently great. A generalized Poisson process of importance in radar and sonar studies is described here and its nth order characteristic functions are specifically obtained, along with its associated first-and second-order moments and covariance function. A variety of examples involving optimum and suboptimum systems such as autoand cross-correlation detectors for signal processing purposes, are used to illustrate the approach to, and departure from, the normality studied more generally in the preceeding sections. Author

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE