Extraction of natural frequency from measured late-time transient responses with rational minimax approximation in frequency domain

A simple technique is presented for extracting natural frequencies from measured late-time transient responses. The method first applies rational mini-max approximation to the Fourier transform of the even extension of a transient response, then obtains natural frequencies directly from the zeros of the denominator polynomial of the optimum rational function. The effectiveness of the method is verified with a synthetic transient response and a measured response of a conducting sphere. The results from the present method for the synthetic transient response are compared with those from the constrained E-pulse technique (CET) and genetic algorithm technique (GAT). It indicates that the present method avoids an initial guess, overcomes the tendency to get stuck in local minima and requires much less computer effort than the CET. In addition, unlike the GAT, it generally guarantees convergence and is insensitive to any parameter.