A theoretical model is developed and exploited for characterizing the behavior of an all-optical circuit that deploys a Fabry-Pérot filter (FPF) and a semiconductor optical amplifier (SOA)-assisted Sagnac switch driven by an intense continuous wave (cw) holding beam to extract the clock signal from a received ultra-fast data stream. The role of each unit is thoroughly studied, and its understanding allows us to identify the critical operational parameters, which include the cw power, the energy of the data pulses, the SOA small signal gain, carrier lifetime and linewidth enhancement factor, the Sagnac loop asymmetry, and the finesse of the FPF. By means of numerical simulation, an extensive set of diagrams is derived, and from their interpretation the impact of these key factors on the amplitude modulation of the extracted clock pulses is investigated and evaluated. This process enables us to appropriately select and combine them to ensure enhanced performance concerning the defined quality metric, first at 10 Gb/s and then at 40 Gb/s. The final outcome demonstrates the technological feasibility and effectiveness of the proposed clock recovery scheme. The obtained results may be useful for theoretically addressing various all-optical signal processing tasks, whose proper execution relies decisively on clock recovery.