Approximation to a Specified Time Response

Author

Yengst, William C.

Volume

9

Issue

2

fYear

1962

fDate

6/1/1962 12:00:00 AM

Firstpage

152

Lastpage

162

Abstract

This paper presents a procedure by which specified data or a function of time $h \\ast (t)$ can be approximated by trigonometric and/or exponential functions of time $h(t)$ for which the Laplace transformations $H(s)$ are known and can be expressed in rational fraction form. The procedure is based on fitting $h \\ast (t)$ by an $m$ thorder difference equation whose coefficients are determined by a least-squares technique. These coefficients are used directly to determine the poles of $H(s)$ . The zeros of $H(s)$ are established by using the prescribed data or function $h \\ast (t)$ and the initial value theorem. The approximate function of time is obtained by taking the inverse Laplace transformation of $H(s)$ . By this procedure not only is an approximation obtained for $h \\ast (t)$ in the time domain, but its transform is also found in rational fraction form suitable for realization as a driving point or transfer function. Furthermore, the least-squares technique used in determining most or all of the unknown parameters in this procedure tends to minimize the effect of random errors or noise present in the specified data.

Keywords

Difference equations; Frequency synthesizers; Helium; Information systems; Laplace equations; Network synthesis; Polynomials; Time factors; Transfer functions; Transient response;

fLanguage

English

Journal_Title

Circuit Theory, IRE Transactions on

Publisher

ieee

ISSN

0096-2007

Type

jour

DOI

10.1109/TCT.1962.1086894

Filename

1086894