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In this paper, we study theoretically the generation of high repetition rate short pulses using fiber optical parametric amplification. We show that the pulse shape and duration depend on the signal location relatively to the pump frequency. We demonstrate that in order to get the shortest pulse width, the signal must be located at one of the extremities of the gain spectrum associated with the pump peak power. We derive the analytical expression of the pulse shape in this case and compare it to the exponential gain regime case. Using numerical simulations, we also analyze the impact of walk-off and pump phase modulation that is required to suppress Stimulated Brillouin Scattering and derive guidelines to design stable train of short and high repetition rate pulses.