Exact sampling results for signals with finite rate of innovation using Strang-Fix conditions and local kernels

Recently, it was shown that it is possible to sample classes of signals with finite rate of innovation. These sampling schemes, however, use kernels with infinite support and this leads to complex and unstable reconstruction algorithms. In this paper, we show that many signals with finite rate of innovation can be sampled and perfectly reconstructed using kernels of compact support and a local reconstruction algorithm. The class of kernels that we can use is very rich and includes any function satisfying Strang-Fix conditions, exponential splines and functions with rational Fourier transforms.