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 ${\mathbb{C}}^N$ 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 $B\le N/2$. 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 $(3N/2+1)$ 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.

虽然频率分辨光门控 (FROG) 广泛用于表征光学中的超快脉冲，但在时频分析和信号处理中经常考虑分析信号，尤其是在提取事件的瞬时特征时。在本文中，我们研究了分析信号的相位检索 (PR) 问题${\mathbb{C}}^N$通过他们的 FROG 测量。建立解析信号FROG-PR的模糊性后，我们发现偶数长度解析信号的FROG-PR与奇数长度解析信号的FROG-PR不同，也与B带限信号的情况不同和$乙\le N/2$. 现有的限带信号方法可以应用于奇数长度的解析信号，但不适用于偶数长度的情况。在两个放松的 FROG-PR 问题和翻译技术的帮助下，我们开发了一种用于偶数长度分析信号的 FROG-PR 方法，并证明在这种情况下通用分析信号可以是唯一的（直到歧义）由他们决定$(3N/2+1)$青蛙测量。相位导数（或瞬时频率）是信号分析的重要特征。作为我们主要结果的应用，建立了一种通过利用模糊性来确定衰减信号的相位导数的方法。