Detecting Signal Structure from Randomly-Sampled Data

Recent theoretical results in Compressive Sensing (CS) show that sparse (or compressible) signals can be accurately reconstructed from a reduced set of linear measurements in the form of projections onto random vectors. The associated reconstruction consists of a nonlinear optimization that requires knowledge of the actual projection vectors. This work demonstrates that random time samples of a data stream could be used to identify certain signal features, even when no time reference is available. since random sampling suppresses aliasing a small (sub-Nyquist) set of samples can represent high-bandwidth signals. Simulations were carried out to explore the utility of such a procedure for detecting and classifying signals of interest.