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A least-squares (LS) method for identifying alias components of discrete linear periodically time-varying (LPTV) systems is proposed. The authors apply a periodic input signal to a finite impulse response (FIR) - LPTV system and measure the noise-contaminated output. The output of this LPTV system has the same period as the input when the period of the input signal is a multiple of the period of the LPTV system. The authors show that the input and the output can be related by using the discrete Fourier transform. In the frequency domain, an LS method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR) - LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.