Frequency analysis via the method of moment functionals

The authors present the use of modulating functions in the context of the nonparametric system identification problem. The proposed method uses the frequency content in short data lengths to set up at least squares estimation of the transfer function at selected frequencies. Since short data lengths are used, there is no assumption of steady-state operation or stationarity of the data, though sufficient energy content in the data at the specified frequencies must be present in order to avoid degeneracy in the least squares estimate. The basis of the technique is the classical Shinbrot method of moment functionals, also known as the modulating function technique, using complex Fourier-based modulating functions. An example illustrating the application of the proposed approach is presented