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The generalized sampling problem is considered using a filter bank model with a stochastic process framework and 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 this stochastic model approach to find a minimized error solution allows consideration of sampling problems that deterministic approaches cannot solve.

A band-limited signal can be recovered from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. A multirate filter bank structure is used to both model this nonuniform sampling (through the analysis bank) and reconstruct a uniformly sampled sequence (through the synthesis bank). Several techniques for modeling the nonuniform sampling are presented for various cases of sampling. Conditions on the filter bank structure are used to accurately reconstruct uniform samples of the input signal at the Nyquist rate. Several examples and simulation results are presented, with emphasis on forms of nonuniform sampling that may be useful in mixed-signal integrated circuits. Index Terms--Bunched sampling, multirate signal processing, nonuniform sampling, time-interleaved analog-to-digital converters.