Properties for state-transition matrix of LPTV two-dimensional filter

Some new properties are derived for the state-transition matrix (A_kℓ^mn) of an linearly periodically time-varying (LPTV) 2D filter (period (M, N)) that are useful in the analysis of LPTV 2D state-space structures. In particular, a simple method is presented to decompose A_kℓ^mn; and analytic expressions are derived for the z-transform of both A_kℓ^mn, and its sub-sampled counterpart, A_kℓ^mM+p,nN+q.