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Linear periodically time-varying filters are considered as modulators and demodulators for the transmission of analog information over a stationary Gaussian channel. A complete analysis is carried out based on a certain general decomposition of such a filter into a number of branches, each containing a linear time-invariant filter and a multiplication with a complex sinusoid. Receiver optimization is carried out under the assumption that the above decomposition is finite. Finally, a joint optimization of transmitter and receiver is derived under the further restriction that the message signal is strictly band-limited.