稀疏多带信号的多速率同步采样
Multirate Synchronous Sampling of Sparse Multiband Signals
摘要：
光学系统的最新进展使其成为对具有高带宽的多频带信号进行欠采样的理想选择。本文提出了一种利用少量采样通道重构多带稀疏信号的新方法。该方案，我们称之为同步多速率采样（SMRS），需要收集样本同步在几个不同的速率，其总和是显着低于奈奎斯特采样率。通过求解线性方程组来重构信号。我们已经证明了一个准确和强大的信号重建使用少量的采样通道，在相对较高的速率。以更高速率采样增加了样本中的信噪比。当采样率增加时，SMRS方案能够显著减少所需的通道数量。我们已经证明，仅使用三个采样通道，一个准确的采样和重建的4个实信号（8波段）。用于在SMRS方案中重构信号的矩阵也具有低条件数。这表明SMRS方案对信号中的噪声是鲁棒的。SMRS方案的成功依赖于采样信号是稀疏的假设。因此，大多数采样频谱在至少一个采样通道中可以是无混叠的。这与多陪集采样方案相反，在多陪集采样方案中，一个通道中的混叠等同于所有通道中的混叠。我们已经证明，SMRS方案获得类似的性能，使用3个采样通道和总采样率8倍的朗道速率的多陪集采样方案的实施，使用6个采样通道的总采样率的朗道速率的13倍。
英文摘要：
Recent advances in optical systems make them ideal for undersampling multiband signals that have high bandwidths. In this paper we propose a new scheme for reconstructing multiband sparse signals using a small number of sampling channels. The scheme, which we call synchronous multirate sampling (SMRS), entails gathering samples synchronously at few different rates whose sum is significantly lower than the Nyquist sampling rate. The signals are reconstructed by solving a system of linear equations. We have demonstrated an accurate and robust reconstruction of signals using a small number of sampling channels that operate at relatively high rates. Sampling at higher rates increases the signal to noise ratio in samples. The SMRS scheme enables a significant reduction in the number of channels required when the sampling rate increases. We have demonstrated, using only three sampling channels, an accurate sampling and reconstruction of 4 real signals (8 bands). The matrices that are used to reconstruct the signals in the SMRS scheme also have low condition numbers. This indicates that the SMRS scheme is robust to noise in signals. The success of the SMRS scheme relies on the assumption that the sampled signals are sparse. As a result most of the sampled spectrum may be unaliased in at least one of the sampling channels. This is in contrast to multicoset sampling schemes in which an alias in one channel is equivalent to an alias in all channels. We have demonstrated that the SMRS scheme obtains similar performance using 3 sampling channels and a total sampling rate 8 times the Landau rate to an implementation of a multicoset sampling scheme that uses 6 sampling channels with a total sampling rate of 13 times the Landau rate.
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