The 1975 paper of Meyer and Burrus gave necessary conditions on the coefficients of a periodically time-varying difference equation to generate a prespecified set of impulse responses. The main contribution of the present paper consists of an algorithm that constructs the coefficients of such a periodically 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 time-invariant system with a periodically time-varying system in such a way that the time-step is preserved. The technique plays an essential role in the ideas underlying the algorithm.