Theory and design of perfect reconstruction transmultiplexers and their relation to perfect reconstruction QMF banks
The theory of transmultiplexers involves the design of 
filters for interconversion between Time Domain Multiplexing (TDM) and Frequency Division Multiplexing (FDM), such that the undesirable Crosstalk is minimized. 
In TDM → FDM → TDM conversion, the perfect reconstruction 
trans-multiplexer (PR-TMUX) achieves complete Crosstalk Cancellation (CC) and is distortion-free. In this 
paper, we present an analysis of the 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 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.