On cross-correlation function evaluation from a periodically time-varying digital filter's output
The aim of the paper is to provide a general, clear, and concise description of the mathematical models supporting the 1D linear, periodically time-varying (LPTV) digital filters. The three representations investigated include linear difference equations, Green's function, and state-space structures. Linear time-invariant equivalent descriptions are then formulated and, 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. It turns out, e.g., that first-order auto-regressive filters are a very particular case of LPTV filters. Comparing and contrasting the results for LPTV filters with similar results for linear time-invariant filters or other particular processes may provide a better insight into the fundamental properties of LPTV systems.
scientific article; zbMATH DE number 1234720
scientific article