Sampling signals with finite rate of innovation in the presence of noise
Sampling signals with finite rate of innovation in the presence of noise
复制标题
在存在噪声的情况下以有限创新率对信号进行采样
DOI：
10.1109/icassp.2009.4960240
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
F. Homann
中科院分区：
文献类型：
--
作者：
P. Dragotti;F. Homann
最近，它已被证明，它是可能的采样非带限信号，拥有有限数量的自由度和唯一地重建它们从有限数量的均匀样本。这些信号包括Dirac流等。本文研究了Diracs流的新息参数的估计问题，该问题是从其噪声样本中提取多项式或指数再生核的。对于一个狄拉克的情况下，我们提供了精确的表达式，这个估计问题的Cramér-Rao界。此外，我们提出的方法来重建一个单一的狄拉克的位置，达到最佳性能的无偏Cramér-Rao界下降到5dB的噪声水平。
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 Cramér- 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 Cramér-Rao bounds down to noise levels of 5dB.