Starting from the derived expression of the Bogoliubov transformation for a broadband pulsed pump, we theoretically characterize the heralded single-photon source, which is based on the signal and idler photon pairs produced in optical fiber via spontaneous four-wave mixing by a pulsed pump. The second-order intensity correlation function, heralding efficiency, indistinguishability, and brightness of the heralded single photons as a function of source parameters, are analyzed and discussed. The validity of the theoretical analysis and calculations are confirmed by the experimental results. The investigations are useful for optimizing the source parameters and for developing a single-photon source suitable for quantum-information processing.