Input reconstruction from oversampled multi-channel data

The authors consider the problem of multichannel sampling for the case in which the input signal bandwidth is smaller than the maximum possible that allows exact recovery (from sub-Nyquist samples taken uniformly from each channel). They focus on this reduced bandwidth case for two channels. They show that, for this case, the conditions which the prefilters must satisfy are less restrictive in some parts of the frequency axis, compared to the full bandwidth case. For a given set of valid prefilters, there is a family of possible postfilters which allows exact recovery of the input, rather than one choice, as in the standard case. It is shown that, if the samples are corrupted by additive white random noise sequence values, the extra flexibility of the postfilters can be used to select an optimal choice that minimizes the reconstruction noise power. An example is provided in which a standard ill-posed reconstruction system can be replaced with one that leads to a well-posed reconstruction when the input is of reduced bandwidth