Optimal generalized sampling expansion

This work presents an analysis of Papoulis' (1977) generalized sampling expansion (GSE) for a wide-sense stationary signal with a known power spectrum in the presence of quantization noise. We find the necessary and sufficient conditions for a GSE system to produce the minimum mean squared error while using the optimal linear estimation filter. This is actually an extension of the optimal linear equalizer (linear source/channel optimization) to the case of M parallel channels.