FROG-measurement based phase retrieval for analytic signals
FROG-measurement based phase retrieval for analytic signals
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DOI：
10.1016/j.acha.2021.05.005
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Youfa Li;Yaoshuai Ma;D. Han
中科院分区：
文献类型：
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作者：
Youfa Li;Yaoshuai Ma;D. Han
频率分辨光门（FROG）在光学中被广泛用于表征超快脉冲，但在时频分析和信号处理中，特别是在提取事件的瞬时特征时，常常需要考虑解析信号。在本文中，我们研究相位恢复（PR）问题的解析信号在C N的FROG测量。在建立解析信号的FROG-PR的模糊性后，我们发现偶数长度解析信号的FROG-PR不同于奇数长度解析信号的FROG-PR，也不同于B≤ N/2的B带限信号的FROG-PR。现有的带限信号的方法可以应用于奇数长度的解析信号，但它不适用于偶数长度的情况。借助于两个放松的FROG-PR问题和一种平移技术，我们发展了一种求解偶数长度解析信号的FROG-PR的方法，并证明了在这种情况下，一般解析信号可以由它们的（3 N/2+ 1）FROG测量唯一地确定（直到模糊度）.相位导数（或瞬时频率）是信号分析的重要特征。作为我们的主要结果的应用，建立了一种方法来确定衰减信号的相位导数，利用模糊度。
While frequency-resolved optical gating (FROG) is widely used in characterizing the ultrafast pulse in optics, analytic signals are often considered in time-frequency analysis and signal processing, especially when extracting instantaneous features of events. In this paper we examine the phase retrieval (PR) problem of analytic signals in C N by their FROG measurements. After establishing the ambiguity of the FROG-PR of analytic signals, we found that the FROG-PR of analytic signals of even lengths is different from that of analytic signals of odd lengths, and it is also different from the case of B-bandlimited signals with B≤ N/2. The existing approach to bandlimited signals can be applied to analytic signals of odd lengths, but it does not apply to the even length case. With the help of two relaxed FROG-PR problems and a translation technique, we develop an approach to FROG-PR for the analytic signals of even lengths, and prove that in this case the generic analytic signals can be uniquely (up to the ambiguity) determined by their (3 N/2+ 1) FROG measurements. Phase derivative (or instantaneous frequency) is a significant feature for signal analysis. As an application of our main result, an approach is established to determine the phase derivatives of decaying signals by exploiting the ambiguity.