# Accession Number:

## ADA158815

# Title:

## Applications of Differential Phase Statistics to Studies of C3 and Spread Spectrum Communications.

# Descriptive Note:

## Final rept.,

# Corporate Author:

## RANDOM APPLICATIONS INC MONTROSE CO

# Personal Author(s):

# Report Date:

## 1985-01-01

# Pagination or Media Count:

## 4.0

# Abstract:

Three reports have been written under this second year of the contract and are listed in the next section as Papers No. 6, 7, 8. Paper No. 6 addresses the classical and very complicated problem of finding the probability density function at the output of an RC filter when the input is a binary random telegraph signal whose intervals are described by a renewal process. Paper No. 7 focuses on a particular case in which the desired probability density is the solution of a rather formidable third-order differential equation with non-constant coefficients. A closed form solution is found for one special value of a system characteristics parameter, and a series solution is obtained for general values of the this parameter. Paper No. 8 is concerned with developing methods for calculating the solution to a fourth order differential equation. Although the theory of such equations is well known, a prohibitive amount of algebra is required to determine the coefficients in series solutions, and a computer method is developed in which the algebra is circumvented. The method is quite general, and in an appendix is applied to Bessels differential equation and, quite surprisingly, a new second solution to Bessels equation is obtained which does not appear to have been previously noticed.

# Descriptors:

# Subject Categories:

- Non-Radio Communications