Approximation in the time domain when transfer-function poles are preassigned

Parseval´s theorem gives the possibility of connecting the approximation in the time domain in the sense of least squares with the corresponding approximation in the frequency domain. If the poles of the approximating transfer function are known or preassigned (as it can be in the case of active RC-synthesis) the best location of its zeros can be obtained with the help of the proposed Lagrange-wise ratio. The location of the transfer-function poles can be evaluated, for example, by the decomposition of hyperbolic functions into infinite products; the location of zeros is obtained as the numerator of the above-mentioned ratio at the second stage of the approximation process. The example shows that the combination of these two steps in the frequency domain can give rise to very satisfactory time-domain approximation.