مرکز منطقه ای اطلاع رساني علوم و فناوري - Approximation to a Specified Time Response

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.