Universal sampling of signals with finite rate of innovation
Recently it has been shown that specific classes of non-bandlimited signals known as signals with finite rate of innovation (FRI) can be perfectly reconstructed by using appropriate sampling kernels and reconstruction schemes. This exact FRI framework was later extended to an approximate FRI framework that works with any kernel. Reconstruction is achieved by recovering all the parameters in the parametric model of the incoming signal, hence it is essential to know the model order (the rate of innovation) to ensure recovery. In view of this, we devise an algorithm for identifying the rate of innovation in order to extend the current sampling scheme to a universal one which enables sampling signals with arbitrary FRI using any acquisition device. Our proposed algorithm can effectively identify the rate of innovation prior to the signal reconstruction using arbitrary kernels and in different noise levels where we also show that it achieves the performance predicted by the Cramèr-Rao bounds.