Forward and reverse transfer function model synthesis

A process for synthesizing a mathematical model for a linear mechanical system using the forward and reverse Fourier transform functions is described. The differential equation for a system model is given. The Bode conversion of the differential equation, and the frequency and time-domain optimization matching of the model to the forward and reverse transform functions using the geometric simplex method of Nelder and Mead (1965) are examined. The effect of the window function on the linear mechanical system is analyzed. The model is applied to two examples; in one the signal damps down before the end of the time window and in the second the signal has significant energy at the end of the time window.