# Accession Number:

## AD0291564

# Title:

## IMPULSE RESPONSE SYNTHESIS FOR NETWORKS CHARACTERIZED BY FUNCTIONS OF A FIRST-ORDER, LINEAR OPERATOR

# Descriptive Note:

# Corporate Author:

## MICHIGAN UNIV ANN ARBOR

# Personal Author(s):

# Report Date:

## 1962-10-01

# Pagination or Media Count:

## 1.0

# Abstract:

The use is considered of integral transforms in the synthesis of time-varying networks for a given impulse response. The cla f networks considered consists of all those containing a finite number of fixed resistances and timevarying reactances, with every reactive element varying in the same way. Such networks are characterized by finite linear combinations ofA FIRST ORDER, LINEAR OPERATOR. Using an integral transform developed by Wattenburg, network function h9l, which are rational functions of the transform variable, l, can be obtained for networks in this class. Conversely, if a rational network function and the corresponding linear operator are given, a network realization can be obtained by well-known methods. In synthesizing a network realizing a prescribed impulse response, ht, tau, neither the rational network function nor the linear operator is known. This report presents a method of finding the operator corresponding to a given ht, tau, and from this finding the network function Hl. Necessary conditions for the realizability of a given ht, tau by a network in the class considered here are presented. Author