This paper presents a least squares desi n methodology for filtering periodically correlated hC) scalar time series. A PC scalar time series can be represented as a WSS vector time series and equivalently any WSS vector time series can be represented as a PC scalar time series. Multirate filter banks and their equivalent polyphase realizations provide a natural mechanism for the bidirectional transition between these two representations. This equivalence provides a spectral representation for PC scalar time series via the spectral representation for WSS vector time series. Using a spectral factorization algorithm for WSS vector processes we can build causal synthesis and causal whitening (innovations) filters for PC scalar time series given the PSD matrix for the equivalent WSS vector process. These techniques are exploited to solve a generalized linear MMSE filter design problem for PC scalar time series. The resulting causal MMSE filter can be implemented as a multirate filter bank structure or an equivalent polyphase structure.
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