The calculation of the coefficients of linear system transfer function with the lumped constant parameters which corresponds to the preset frequency response is present.

Calculation of the transfer function on a given frequency response is the optimization problem. Direct solution has multiextremal nonlinear optimization.

Hilbert transform is applied to calculate the minimum-phase phase response. Therefore, the optimization problem of calculating the coefficients of the transfer function has complex goal function with some restrictions.

An example of the synthesis transfer function of the order seven for a given frequency response of real parametric amplifier is present. We obtain repeatability of the frequency response of less than 3 %.

All calculations is made in the system MATLAB.

1. Matviychuk Yaroslav, Mathematical macromodelling of dynamic systems: theory and application, Lviv, 2000. 215 p., (in ukrainian), http://ena.lp.edu.ua:8080/handle/ntb/22710. 2. Byeong Ho Eom, Peter K. Day, Henry G. LeDuc and Jonas Zmuidzinas, A wideband, low-noise superconducting amplifier with high dynamic range, NATURE PHYSICS, vol.8, august 2012, p. 623–627.