Time-frequency transfer function and realization algorithm for discrete periodic linear systems
P.B. Park, Erik I. Verriest · 2002
A realization of a linear periodically time-varying system of order n with m inputs, p outputs and period N is given by x(k+1)=A/sub [/k]x(k)+B/sub [/k]u(k), y(k)=C/sub [/k]x(k)+D/sub [/k]u(k), Where [k] = k mod N. The parameters of the realization are denoted by ((A/sub k/, B/sub k/, C/sub k/, D/sub k/))N. The construction of a state variable representation, from a given pulse response, is outlined. Time-frequency analysis/synthesis transfer function are defined by means of proper z-transforms of the pulse response h(l,r), and their N-phase decomposition is introduced. The realisation problem is reduced to solving the matrix equation H/sub e/(z)=C/sub e/(zI-A/sub e/)/sup -/1B/sub e/+D/sub e/ where H/sub e/(z) is the extended matrix transfer function constructed from h(l,r) through the N-phase decomposition F(l,z) or G(z,r).>