多频带信号的正则化采样
Regularized sampling of multiband signals
摘要：
本文提出了一种多带信号的正则化采样方法，使其在接近朗道极限的同时保持对噪声的低敏感性。该方法是基于带限窗口，其次是三角近似在连续的时间间隔。关键是三角近似“继承”了多带特性，即其系数由对应于多带分量的非零元素的突发形成。结果表明，该方法可以很好地结合最近提出的同步多速率采样（SMRS）计划，给定的线性系统是稀疏的，由1和0形成。所提出的方法允许一个贸易采样效率的噪声灵敏度，特别适合于有界信号与无界的能量，如在通信，导航，音频系统等，此外，它也适用于有限能量信号和周期性带限信号（三角多项式）。本文提出了一种盲估计多带信号及其分量支持度的子空间方法，并通过数值算例对结果进行了验证。
英文摘要：
This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of non-zero elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multi-rate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.
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