Abstract
Concise mathematical models are established for one-dimensional, linear, periodically time-varying digital filters. The three representations considered include linear difference equations, Green's function, and state-space structures. Linear time-invariant equivalent descriptions are then formulated, and from these, for the particular case of a white noise input, various analytical expressions are derived for both the cross-power spectral density functions and cross-correlation functions of the filter's subsampled output. These results are compared and contrasted with similar formulas for a linear time-invariant system.
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McLernon, D.C. On cross-correlation function evaluation from a periodically time-varying digital filter's output. Circuits Systems and Signal Process 17, 495–515 (1998). https://doi.org/10.1007/BF01201505
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DOI: https://doi.org/10.1007/BF01201505