A performance analysis of an optical clock extraction circuit based on a Fabry-Perot filter (FPF) is presented. Two analytical methods, time-domain and frequency-domain analysis, are developed in this paper. Time-domain analysis shows that there is no phase jitter in the extracted optical clock if the free spectral range (FSR) of the FPF is exactly equal to the signal clock frequency. Based on this, we obtain an analytical expression for root mean square (rms) amplitude jitter of the extracted optical clock in time domain, in which we have taken the impacts of carrier frequency drift and carrier phase noise into account. When the FSR of the FPF deviates from the signal clock frequency, both phase jitter and amplitude jitter will occur in the extracted optical clock. In this situation, a more general frequency-domain method is developed to deal with the timing performance under the assumption that carrier phase noise is negligible. This method allows us to calculate both rms phase jitter and rms amplitude jitter of the extracted optical clock. Using the developed two methods, we present a detailed numerical investigation on the impacts of finesse of the FPF, carrier frequency drift, resonator detuning, carrier phase noise, and optical pulse chirp on the timing performance. Finally, the application of this circuit in multiwavelength clock recovery is discussed.