Design of multichannel nonuniform transmultiplexers using general building blocks

The paper considers design of multichannel, nonuniform-band transmultiplexers. It is well known that using traditional building blocks-up and downsamplers and linear time-invariant (LTI), causal filters-nonuniform transmultiplexers typically do not achieve perfect reconstruction. To alleviate this, we propose to build nonuniform transmultiplexers using general dual-rate structures that provide more design freedom, and hence, perfect reconstruction can be achieved. 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 that 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 that has good frequency-limiting properties in the synthesis end and is very close to perfect reconstruction