The technique of polyphase filterbanks is commonly used for signal processing in radio astronomy. The rapid and ongoing evolution of parallel hardware architectures requires optimised implementations of such techniques to be redeveloped. However, much of the published research regarding polyphase filterbanks refers the reader to signal processing books with a more general scope. Furthermore, these references tend to focus on the design of filters, rather than their implementation. For this reason, this work presents a mathematical background for the implementation of a polyphase filterbank specific to radio astronomy. It also addresses the advantages and disadvantages of polyphase filterbanks in comparison with more commonly used techniques.