# Accession Number:

## AD0813741

# Title:

## DIGITAL FILTER SYNTHESIS.

# Descriptive Note:

## Final rept. 17 Dec 65-20 Jan 67,

# Corporate Author:

## CORNELL AERONAUTICAL LAB INC BUFFALO N Y

# Personal Author(s):

# Report Date:

## 1967-03-01

# Pagination or Media Count:

## 146.0

# Abstract:

This report is concerned with several aspects of digital filter synthesis. Of particular interest is the derivation of the optimal discrete filter to be used in place of a given analog filter so as to result in minimum mean square error of the sampling instants. The spectra of the signals to be filtered are assumed to be either 1 of known rational form, or 2 bandlimited. The condition which the optimal discrete filter must satisfy is obtained by minimizing the expected value of the square of the error, formed by the difference between the discrete and sampled-analog channels. For rational spectra, the optimum discrete filter is a function of both the frequency characteristics of the analog filter and the spectrum of the input signal. The optimal discrete filter for this case can be placed in rational form. For bandlimited spectra, it is demonstrated that the corresponding optimal discrete filter is dependent only upon the frequency characteristics of the analog filter. The optimal discrete filter for this case, however, cannot, in general, be placed in rational form. Several methods are described for placing this optimal discrete filter in rational form. One of these methods, which involves obtaining the best first order rational approximation to the optimum transformation, reduces to the well known Tustin transformation. Author

# Descriptors:

# Subject Categories:

- Electrical and Electronic Equipment
- Numerical Mathematics