A periodically time-varying minimal partial realization algorithm based ontwisting

The 1975 paper of Meyer and Burrus gave necessary conditions on the coeffic ients of a periodically time-varying difference equation to generate a pres pecified set of impulse responses. The main contribution of the present pap er consists of an algorithm that constructs the coefficients of such a peri odically time-varying realization of minimal lag. Thus the algorithm solves the minimal partial realization problem for the periodically time-varying (scalar) case. We use a general technique ("twisting") for associating a ti me-invariant system with a periodically time-varying system in such a way t hat the time-step is preserved. The technique plays an essential role in th e ideas underlying the algorithm. (C) 1999 Elsevier Science Ltd. All rights reserved.