On the filter design for a class of multimode transmultiplexers

This paper discusses some issues related to the filter design in a class of multimode transmultiplexers (TMUXs). These TMUXs cover a large set of frequency division multiplexed (FDM) scenarios with simple reconfigurations. The reconfiguration is performed by changing the values of some multipliers. The paper outlines a direct filter design to decrease the level of inter-symbol and inter-carrier interference by the use of time-varying periodic filters. These time-varying periodic filters are derived from the known FDM scenarios and they are included as additional constraints in the filter design. Both minimax and constrained least-squares approaches are treated and it is shown that by including the additional constraints, the level of the TMUX noise can be reduced. This results in a better approximation of perfect reconstruction and makes the filter design direct.