Rational sampling rate conversion in linear multirate digital signal processing systems can be efficiently realised by a matrix of polyphase filters. This paper presents a new analytical approach that simplifies the design of polyphase matrix and associated structures. Instead of a set of procedures and network transformation rules based on signal-flow graphs, the matrix of subfilters is obtained by a simple formula, which contains interpolators and decimators as special cases. Using this approach, it is simple to derive Z-transforms of subfilters, and to minimise delay elements.