Approximation to a Specified Time Response

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.