|M.Sc Student||Lihu Berman|
|Subject||Robust Non-Uniform Sampling of Band-Limited Signals|
|Department||Department of Electrical Engineering||Supervisor||Professor Emeritus Feuer Arie|
|Full Thesis text|
It is a known fact that recurrent non-uniform sampling can be used to achieve, at least asymptotically, minimum-rate sampling of band-limited multi-band signals. Also known is the fact that in such sampling schemes the reconstruction stability is determined by the condition number of the modulation matrix.
This work examines the problem of selecting the best sampling pattern - in the condition number sense - in such schemes, given the spectral support, the average sampling rate, and the number of samples in the recurring pattern.
Unlike previous work, in which a subset of samples is chosen from a uniform high-rate sampling, here we allow the samples to vary continuously, but constrain the pattern to possess a special structure. This enabled us to develop a new pattern selection algorithm which selects all the samples simultaneously, as opposed to the sequential selection of sample locations in other state-of-the-art algorithms.
Simulation results show that our approach is better both in the resulting condition number, and in complexity - measured by the number of criterion computations - for relatively small problems.
In addition, this approach allowed us to derive analytical results. First, we derived a necessary and sufficient condition on the spectral support of a one-dimensional continuous signal, such that the optimal sampling pattern results in perfect conditioning. The optimal sampling pattern for the aforementioned case is given as well. Second, we present a complete characterization of the universal patterns in our approach. This is especially interesting, as the alternatives are either using heuristics, which are not infallible, or performing a brute-force check which is very inefficient in general, and completely unfeasible in any but the smallest problems.
Finally, we extend some of the aforementioned results to multi-dimensional signals.