Transfer function synthesis as a ratio of two complex polynomials

Experimental frequency response data obtained from a linear dynamic system is processed to obtain the transfer function as a ratio of two frequency-dependent polynomials. The difference between the absolute magnitudes of the actual function and the polynomial ratio is the error considered. The polynomial coefficients are evaluated as the result of minimizing the sum of the squares of the above errors at the experimental points. The polynomial coefficients are computed numerically using an IBM 704 FORTRAN program. The magnitude and phase angle of the transfer function are evaluated at the various frequencies, using the computed polynomial ratio; and are compared with the observed data. The method presented here gives an analytic description of the complex transfer function superior to that given by minimization of the "weighted" sum of the squares of the errors in magnitude.