This paper deals with the system for rational sampling rate change. Two efficient implementations are given. The first structure shows the relationship between the polyphase decomposition of the output and the linear, periodically time-varying (LPTV) nature of the system. The second system refines the first one step further to give the polyphase matrix implementation. Frequency domain relations are given for both systems. The first system is a single-input/multi-output time-varying system, and in this case the z-domain relation is not a transfer function. However, the polyphase matrix can be represented as a multi-input/multi- output time-invariant system, and as such has a transfer matrix, which is given.