Phaseless Signal Recovery in Infinite Dimensional Spaces Using Structured Modulations
Phaseless Signal Recovery in Infinite Dimensional Spaces Using Structured Modulations
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DOI：
10.1007/s00041-014-9352-3
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发表时间：
2013-05
影响因子：
1.2
通讯作者：
V. Pohl;Fanny Yang;H. Boche
中科院分区：
文献类型：
--
作者：
V. Pohl;Fanny Yang;H. Boche
本文研究了无限维空间中连续信号从其频率样本的幅值恢复的问题。提出了一种过采样和复指数调制相结合的采样方案。给出了充分的条件，使得几乎每个具有紧凑支持的信号都可以仅使用其频域的幅值样本重构到非模常数。最后表明，平均采样率为奈奎斯特速率的四倍就足以重建几乎每一个时域信号。
This paper considers the recovery of continuous signals in infinite dimensional spaces from the magnitude of their frequency samples. It proposes a sampling scheme which involves a combination of oversampling and modulations with complex exponentials. Sufficient conditions are given such that almost every signal with compact support can be reconstructed up to a unimodular constant using only its magnitude samples in the frequency domain. Finally it is shown that an average sampling rate of four times the Nyquist rate is enough to reconstruct almost every time-limited signal.