On alias-component matrices of discrete-time linear periodically time-varying systems

We first use the Fourier series to find the steady-state response of discrete-time linear periodically time-varying (LPTV) systems to periodic inputs. Then, in order to obtain the response of LPTV systems to general inputs, we use the Fourier transform (FT) and establish a direct link between alias-component matrices and LPTV systems modeled by periodically time varying difference equations. This is given in terms of the Fourier series of the parameters in the model.