# Accession Number:

## AD0705608

# Title:

## HOMOMORPHIC FILTERS FOR CONVOLVED FUNCTIONS,

# Descriptive Note:

# Corporate Author:

## SOUTHERN METHODIST UNIV DALLAS TEX INFORMATION AND CONTROL SCIENCES CENTER

# Personal Author(s):

# Report Date:

## 1969-12-05

# Pagination or Media Count:

## 68.0

# Abstract:

The capabilities of a limited class of non-linear systems have been demonstrated. The convolution in its continuous structure is an integral equation involving two or more time functions. Given the value of this integral, it is usually difficult to evaluate the constituent parts. The homomorphic filters discussed in this work accomplish the filtering process through the principle of generalized superposition. This principle enlarges the applicability of principles of superposition and homogeneity applicable to the well understood linear systems by associating a vector space with the inputs to non-linear systems. It is then possible to define a linear transformation which maps an input space to another vector space. However, the number of useful relationships which correspond to the vector addition for the vector space is limited. The linear transformations have been worked out for multiplication and convolution of input elements, besides the familiar case of algebraic addition which does not require this abstract treatment. This dissertation demonstrates the application of the principle of generalized superposition by separating the probability density functions. The functions considered as those that arise in the F.M. detection process and result from the addition of two independent random variables. Author

# Descriptors:

# Subject Categories:

- Cybernetics