Identification of LPTV systems in the frequency domain

We derive a new method for the identification of discrete linear periodically time-varying (LPTV) systems. Take an LPTV system with period M, and assume that an input with period N is applied to this system, where N is a multiple of M. The output of this system will be periodic with period N. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. We show that the method achieves the Cramer–Rao lower bound (CRLB). A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification. Simulation results illustrate the efficiency of the proposed algorithm.