An analysis is presented of the perfect reconstruction transmultiplexer (PR-TMUX) based on the polyphase component matrices of the filter banks used in TDM → FDM and FDM → TDM conversion respectively. Using that, a necessary and sufficient condition for complete crosstalk cancellation (CC) is obtained. The close relation between PR-TMUX filters and PR-QMF banks is used to obtain a direct design procedure for PR-TMUX filters.