Sampling signals with finite rate of innovation in the presence of noise

Recently, it has been shown that it is possible to sample non-bandlimited signals that possess a limited number of degrees of freedom and uniquely reconstruct them from a finite number of uniform samples. These signals include, amongst others, streams of Diracs. In this paper, we investigate the problem of estimating the innovation parameters of a stream of Diracs from its noisy samples taken with polynomial or exponential reproducing kernels. For the one-Dirac case, we provide exact expressions for the Cram´er- Rao bounds of this estimation problem. Furthermore, we propose methods to reconstruct the location of a single Dirac that reach the optimal performance given by the unbiased Cram´er-Rao bounds down to noise levels of 5dB.

• Type: Conference
• Year: 2009
• Where: ICASSP
• Authors: Pier Luigi Dragotti, Felix Homann
• Keywords: Exponential Reproducing Kernels, ICASSP 2009, Limited Number, Non-bandlimited Signals, Signal Processing