Determination of a transfer function from amplitude frequency response data†

An iterative procedure for determining the transfer function (minimum phase) of a linear system from its amplitude frequency response data is presented. The transfer function is the best in the least-squared-error sense. Frequency response data spanning several decades are weighted evenly, so the procedure gives a good fit at all data points. A magnitude-squared function is first found that best fits the frequency response data, and the minimum-phase transfer function is obtained from the magnitude-squared function by spectral factorization. Examples are used to illustrate the application of this procedure in system reduction and system identification.