Minimum Mean-Squared Error Reconstruction for Generalized Undersampling of Cyclostationary Processes
The generalized sampling problem is considered using a filter bank model with a stochastic process framework. A signal reconstruction solution minimizing the time-averaged mean-squared error is found using a filter bank optimization technique for cyclostationary signals. The use of a stochastic model approach to find a minimized error solution rather than a perfect reconstruction solution allows consideration of sampling problems that deterministic approaches cannot solve. For instance, a particular sampling density is not required, allowing reconstruction optimization in cases of undersampling. An extension is also presented for optimal reconstruction in the presence of additive noise and interference. The result is a generalized sampling model which can be used for an extensive variety of scenarios, combining aspects of undersampling, multiple-input multiple-output (MIMO) sampling, and periodic nonuniform sampling