Multi-channel signal reconstruction using noisy samples

The generalized multichannel sampling theorem of A. Papoulis (1977) assumes a bandlimited signal simultaneously processed by a bank of m linear time-invariant (LTI) prefilters; the filter outputs are then sampled and the original signal recovered from these samples by means of m LTI postfilters. Consideration is given to the stability (well-posedness) of the signal reconstruction with respect to additive noise perturbations of the sample values. It is shown that the reconstruction is stable if and only if the postfilter transfer functions are square integrable, thus proving a converse to the ill-posedness result K.F. Cheung and R.J. Marks (1985) while giving an alternative proof of their theorem