Periodic non-uniform sampling for FRI signals

A typical finite-rate-of-innovation (FRI) signal reconstruction scheme is based on the measurement of uniform samples in time/frequency domain, and the application of the annihilating filter on the measured samples. We propose a continuous-time annihilation framework for a class of FRI signals. In particular, we show that FRI signals of sum-of-weighted exponential form can be annihilated by a composition of translation operators and show that the parameters of the signal can be estimated in the periodic non-uniform sampling (PNU) scenario. We discuss the advantages of PNU sampling over uniform sampling and extend it for general FRI signal sampling and reconstruction. Simulations are performed and the results are compared with state-of-the-art methods for signal-to-noise ratios ranging from -20 to 100 dB. An improvement in the estimation accuracy of 15-55 dB in terms of bias and mean-square error is achieved over conventional methods by a rearrangement of uniform samples to follow PNU sampling.