A new method to compute optimal periodic sampling patterns

It is possible to reconstruct a signal from cyclic nonuniform samples and thus take advantage of a lower sampling rate than the Nyquist rate. However, this has the potential drawback of amplifying signal perturbations, e.g. due to noise and quantization. We propose an algorithm based on sparse reconstruction techniques, which is able to find the sparsest sampling pattern that permits perfect reconstruction of the sampled signal. The result of our algorithm with a proper constraint values is a sparse subset of samples that results in an ideal condition number for its equivalent sub-DFT matrix. Besides, our algorithm has low complexity in terms of computation. The method is illustrated by simulations for a sparse multi band signal.