Optimal design of general multi-channel nonuniform transmultiplexers

The paper considers the design of multi-channel, nonuniform-band transmultiplexers. To achieve perfect reconstruction, we propose to build nonuniform transmultiplexers using general dual-rate structures which provide more design freedom. Such general transmultiplexers have a new source of error called aliasing distortion, in addition to the traditional cross-talk, magnitude, and phase distortions. We propose a composite error criterion which captures all four distortions in one. Using this error criterion as reconstruction performance measure, we develop an optimal design procedure and apply it to a three-channel nonuniform example, yielding an FIR transmultiplexer which has good frequency limiting properties in the synthesis end and is very close to perfect reconstruction.