# Accession Number:

## AD0658862

# Title:

## OPTIMUM LINEAR INTERPOLATION OF SAMPLED FUNCTIONS,

# Descriptive Note:

# Corporate Author:

## NORTHEASTERN UNIV BOSTON MASS COMMUNICATION THEORY GROUP

# Personal Author(s):

# Report Date:

## 1967-04-01

# Pagination or Media Count:

## 73.0

# Abstract:

A study of linear interpolation of sampled random processes is presented in this report. A mathematical model of a sampler and of an interpolator are first developed. These models are used to derive general expressions for the mean-square interpolation error. The specific examples of zero- and first-order interpolation are used to illustrate the expressions. The problem of optimum interpolation is then formulated using the criterion that the mean-square error be a minimum. Explicit expressions for the optimum causal linear filter for interpolation using corrupted samples and expressions for the resulting minimum mean-square error are obtained. These results are illustrated by some specific examples of practical importance. A simple upper bound of the mean-square error is derived and a generalization of the sampling theorem for random functions is obtained by use of this bound. Although the important case of periodic sampling is emphasized in this report, the extension to a periodic sampling is given. Author

# Descriptors:

# Subject Categories:

- Operations Research
- Cybernetics