Identification of linear periodically time-varying systems using periodic sequences

A new method for the identification of discrete linear periodically time-varying (LPTV) systems is derived in this paper. 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 the problem of identification of LPTV systems can be formulated in the frequency domain. By using the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. Simulation results illustrate the efficiency of the proposed algorithm.