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Previous studies have revealed that, modulation instability (MI) in optical fibers is an all-optical technology to generate high repetition rate pulse trains which found applications in high-speed optical communication systems.Conventionally, one usually numerically demonstrates MI based generation of high-repetition-rate pulse trains with the input corresponding to the continuous-wave with weak sinusoidal modulation imposed on it, which means the corresponding frequency spectrum of the initial optical perturbation has been assumed to be discrete.Generally speaking, however, the spectrum of the initial optical perturbations such as pulse perturbation may be continuous.Thus, we numerically demonstrate MI based generation of high-repetition-rate optical pulse trains by using the optical wave with its phase perturbed by Gaussian-typed continuous spectrum.The shape and frequency spectrum evolutionsof this continuous spectrum perturbed optical wave are numerically investigated.The results show that, the generated pulse trains consist of limited number of pulses which are generally not equal in width, intensity, and interval.Moreover, when the other parameters are the same, the positive quintic nonlinearity can make the pulse width and interval shorten which thus means the positive quintic nonlinearity is beneficial to generate higher repetition rate pulse trains.While the negative one takes the opposite.The corresponding amplitude frequency spectra take on obvious MI characteristics and will develop from the initial smooth profiles to the two-peak and then multi-peak structure.The developed chirp during the generation process of pulse trains is numerically simulated as well.