Lumped parametric system models are simplified and computationally advantageous in the frequency domain of linear systems. Nonlinear least squares computer program finds the least square best estimate for any number of parameters in an arbitrarily complicated model

Hays, J. R.

English

NASA Technical Reports Server

December 1969	 Brief 69-10577 
NASA TECH BRIEF	 1 
NASA Tech Briefs are issued to summarize specific innovations derived from the U.S. space program, 
to encourage their commercial application. Copies are available to the public at 15 cents each 
from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Frequency Domain Analysis and Synthesis of Lumped Parameter Systems

Using Nonlinear Least Squares Techniques 
A generalized technique for the design and analysis 
of linear systems in the frequency domain has been 
developed that greatly improves the design procedure 
for filter and compensation circuits. The evaluation 
of lumped parametric system models has been found 
to be simplified and computationally advantageous in 
the frequency domain. 
The numerical Fourier transformation equations 
involved in the frequency domain model are ideally 
suited for computer calculations. A nonlinear least 
squares computer program has been developed which 
finds the least square best estimate for any number 
of parameters in an arbitrarily complicated model. 
Additional advantages of frequency domain model-
ing include: the facility with which analytical fre-
quency solutions can be obtained as compared with 
time solutions; there is no change in the form of the 
frequency solution as the values of the parameters
are changed; the limits of the integral of the squared 
error can be set to include only the region of interest. 
Note: 
No further documentation is available. Inquiries 
may be directed to: 
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B69- 10577 
Patent status: 
Inquiries about obtaining rights for the commercial 
use of this invention may be made to NASA, Code 
GP, Washington, D.C. 20546. 
Source: James R. Hays of

The Boeing Company
under contract to

Marshall Space Flight Center

(MFS- 15033) 
Category 02 
This document was prepared under the sponsorship of the National 	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
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Frequency domain analysis and synthesis of lumped parameter systems using nonlinear least squares techniques

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