Robust Patterns in Recurrent Sampling of Multiband Signals

Periodic nonuniform sampling can be used to achieve sub-Nyquist sampling of bandlimited multiband signals. In this paper, we examine the question of selecting the sampling pattern in such a scheme, so that the reconstruction robustness - measured by the condition-number of the modulation matrix - is maximized. Contrary to previous work, where the sampling pattern was chosen from a discrete set, we let the sampling patterns vary continuously, but impose a structural constraint. Using this approach, we derive necessary and sufficient conditions on the spectral support of the signal for which perfect conditioning exist, namely, for which a sampling pattern can be found so that the resulting modulation matrix has a condition number equal to 1. A simple test to check for these conditions is developed and the desired sampling patterns are found. An algorithm for choosing the sampling pattern when the aforementioned conditions are not satisfied is also introduced. Finally, we present some simulation results.