Design of multichannel nonuniform transmultiplexers using general buildingblocks

The paper considers design of multichannel, nonuniform-band transmultiplexe rs, It is well known that using traditional building blocks-up- and downsam plers and linear time-invariant (LTI), causal filters-nonuniform transmulti plexers typically do not achieve perfect reconstruction. To alleviate this, we propose to build nonuniform transmultiplexers using general dual-rate s tructures that provide more design freedom, and hence, perfect reconstructi on can be achieved. Such general transmultiplexers have a new source of err or called aliasing distortion in addition to the traditional cross-talk, ma gnitude, and phase distortions. We propose a composite error criterion that captures all four distortions in one. Using this error criterion as recons truction performance measure, we develop an optimal design procedure and ap ply it to a three-channel nonuniform example, yielding an FIR transmultiple xer that has good frequency-limiting properties in the synthesis end and is very close to perfect reconstruction.