# Mathematical Modelling of a First Order Transducer

## Document Type

Thesis - Open Access

1970

## Degree Name

Master of Science (MS)

## Department / School

Electrical Engineering

## Abstract

First chapter lays the ground work for this research paper. The problem is posed immediately, enabling the reader to gain a better appreciation of the material that follows. The next article explains the thought process that motivated this problem. This is followed by reviewing the available. literature in the field and on which the author has relied quite extensively. The chapter concludes by explaining the more common terminology which will be used frequently throughout the dissertation. Given a configuration of linear, passive network elements, termed filter, how faithful a reproduction of the input process is the process at the output of a first order transducer? Or, in other words, how much information is lost in a filter? This problem arises due to the necessity of using a filter in a system --- either for reasons of convenience or by force of circumstances. The paper attempts to model a transducer mathematically and to express the input and output processes statistically. In order to-do so, a meaningful measure of error should be chosen and defined. The error measure chosen is the Mean-Integral. Square Error (MISER). A very good approximation of the situation is the existence of the signal for a long period of time with respect to the time constants of the filter. The problem then lends itself to what is known as steady state analysis. This work is restricted to analyzing the pattern given a random Stationary Gaussian Markoff (SGM) process. An expression to calculate the MISER will be developed and a method to computerize the same will be indicated. However, actual numerical computations will be deferred. The expression for MISER will establish a relationship between the location of a pole and/or zero and the magnitude of MISER. The use of the SGM process as the input, enables one to describe output process in a concise manner. It also enables the results of this study to be compared with the results of others in related fields who have used the SGM process as a signal source.

## Library of Congress Subject Headings

Transducers

Mathematical models

South Dakota State University Theses

application/pdf

118

## Publisher

South Dakota State University

COinS