Triggerless Random Interleaved Sampling

A single short sequence of samples taken at sub-Nyquist rate rarely allows for periodic signal recovery. If there is more than one such sequence and time offsets between these sequences are given, the signal approximation is possible and is known as equivalent time or interleaved sampling. If the inter-sequence time offsets are not known, one can still benefit from multiple sequences. We show that periodic signals are determined by the probabilistic distribution of their sample sequences, provided that the inter-sequence offsets are uniformly distributed (in a probabilistic sense). We also show how to estimate periodic signals in a real scenario, when instead of the probabilistic distribution, only a finite number of such sequences are given. The proposed method is verified using a computer simulation.