Irregular sampling with unknown locations

Abstract

This paper is concerned with finding the locations of an irregularly sampled finite discrete-time band-limited signal. First a geometrical approach is described and is transformed into an optimization problem. Due to the structure of the problem, multiple solutions exist and are shifts of each other. Three methods of solution are suggested: an exhaustive method which finds the exact set of locations; random search method and cyclic coordinate method, both descent methods, which find approximate or exact solutions. The cyclic coordinate method is less likely to fall in a local minimum and proves to be more satisfactory than the random search method in the presence of jitter. A practical example, where a signal is sampled several times with a regular spacing, is also described.