SOME RESULTS IN THE THEORY OF CROSSTALK-FREE TRANSMULTIPLEXERS

The theory of transmultiplexers involves the design of filters for time domain multiplexing (TDM) arrow pointing left and right frequency division multiplexing (FDM) interconversion such that the undesirable crosstalk is minimized. The crosstalk-free transmultiplexer (CF-TMUX) focuses on crosstalk cancellation (CC) rather than on suppressing it. In this paper, we present an analysis of the CF-TMUX based on the polyphase component matrices of the filter banks used in TDM --> FDM and FDM --> TDM conversions, respectively. Thus a necessary and sufficient condition for complete CC is obtained. It is shown that the filters for a CF-TMUX are the same as the filters for a 1-skewed alias-free QMF bank. In addition, if the QMF bank satisfies the perfect reconstruction (PR) property, then the TMUX also satisfies PR. The relation between CF-TMUX filters and alias-free QMF banks is used to obtain a direct design procedure for CF-TMUX filters (both FIR and IIR). It is also shown that we can obtain approximately crosstalk-free TMUX filters from any approximately alias-free QMF bank. Design examples and comparison tables are included.