# Accession Number:

## AD0259196

# Title:

## THE USE OF A CLASS OF NONLINEAR SYSTEMS IN THE PROBLEM OF OPTIMUM FILTERING

# Descriptive Note:

# Corporate Author:

## COLUMBIA UNIV NEW YORK SCHOOL OF ENGINEERING AND APPLIED SCIENCE

# Personal Author(s):

# Report Date:

## 1961-05-01

# Pagination or Media Count:

## 1.0

# Abstract:

The input and output of a class N1 system are related by an integral whose kernel is a function of 2 variables. The 2 variables are the amplitude of the input and the elasped time since the input isapplied. Only stationary inputs are considered. Three aspects of the problems are considered. The first concerns the design of optimum filters for given inputs. Integral equations relating the form of the optimum filter and the statistics of the inputs are derived. A method is developed for the solution of the resulting optimizing integral equations it includes a sufficient condition under which the solution so obtained corresponds to an optimum system which satisfies the conventional stability condition. The second part takes an unconventional approach to the problem of optimum filtering. It is concerned with the search for a class of message processes for a given noise and a prescribed filter such that the given filter is the optimum least square filter. The last aspect deals with a study of correlation functions. Some properties of the cross-correlation function between the outputs of a pair of class N1 systems are investigated. In addition, consideration is given, to the problem of identifying an unknown class N1. It is shown that the power density spectrum of the response of this unknown system to correlated Gaussian test inputs completely specifies the system. Author