Perfect transmultiplexers
The mathematical equivalence of transmultiplexers and sub-band coders with reconstruction of the original signals is shown. Critical time sampling in sub-band coders corresponds to critical frequency sampling in transmultiplexers. In both cases, non-ideal band-pass filters are sufficient to reconstruct the original signals without aliasing (in sub-band coders) and without crosstalk (in transmultiplexers). The equivalence between the two systems allows the use of results from sub-band coders (like the QMF and pseudo-QMF concepts) for the design of transmultiplexers. The price to be paid is a synchronous up- and down-sampling between transmitter and receiver, as well as a good channel characteristic. Simulation results are given for the non-ideal case. All results are obtained through a matrix analysis of the filter bank problem.