  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 $\Bbb{C}^N$ 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 $B \leq N/2$. 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.
