Near-Optimal Bounds for Signal Recovery from Blind Phaseless Periodic Short-Time Fourier Transform
Near-Optimal Bounds for Signal Recovery from Blind Phaseless Periodic Short-Time Fourier Transform
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DOI：
10.1007/s00041-022-09983-x
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发表时间：
2021-12
影响因子：
1.2
通讯作者：
Tamir Bendory;Chi Y. Cheng;D. Edidin
中科院分区：
文献类型：
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作者：
Tamir Bendory;Chi Y. Cheng;D. Edidin
我们研究了从无相位周期短时傅里叶变换（STFT）的样本中恢复信号的问题：信号的傅里叶变换的幅度乘以滑动窗口。我们表明，如果windowwis已知的，那么一个通用的信号可以恢复，到一个全球的相位，从小于4Nphaseless STFT测量。在盲的情况下，当窗口是未知的，我们表明，信号和窗口可以同时确定，一组不可避免的模糊度，从不到测量。在这两种情况下，我们的边界都是最优的，直到一个小于2的常数。
We study the problem of recovering a signalfrom samples of its phaseless periodic short-time Fourier transform (STFT): the magnitude of the Fourier transform of the signal multiplied by a sliding window. We show that if the windowwis known, then a generic signal can be recovered, up to a global phase, from less than 4Nphaseless STFT measurements. In the blind case, when the window is unknown, we show that the signal and the window can be determined simultaneously, up to a group of unavoidable ambiguities, from less thanmeasurements. In both cases, our bounds are optimal, up to a constant smaller than two.