DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click

HERE to register or log in.

# Accession Number:

## AD0626449

# Title:

## LINEAR FILTER OPTIMIZATION WITH GAME THEORY CONSIDERATIONS

# Descriptive Note:

# Corporate Author:

## JOHNS HOPKINS UNIV LAUREL MD APPLIED PHYSICS LAB

# Report Date:

## 1955-03-01

# Pagination or Media Count:

##
16.0

# Abstract:

## The optimum reproduction of a signal in the presence of noise by means of linear filters is considered when the signal is unknown. The problem is likened to a game. In such a game the signal spectrum can be considered to be the strategy of one of the participants, while the strategy of the other participant is specified by the transfer function of the filter. The payoff is taken to be the mean square difference between filter output and signal. The signal producer by his choice of spectrum attempts to maximize the difference while the filter designer attempts to minimize it. In order to obtain game theory solutions the optimum transfer function for any fixed signal spectrum and also the optimum signal spectrum for any allowable transfer function are found. The game theory solution is then the intersection of these two functional equations. In order to obtain the optimum transfer function for any fixed signal spectrum in a convenient form a new variational procedure has been developed which yields an integral equation for the amplitude of the transfer function. The form of the relationship is dependent only on the noise spectrum. For simple noise spectra the results are both simple and convenient for game theory solutions.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#