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A general analytic solution for Brillouin distributed fibre sensors with sub-meter spatial resolution has been obtained by solving the coupled wave equation by a perturbation method. The effect of the interaction of a square pump pulse with a continuous signal is described in full generality for all possible pumping schemes and for any detuning with the resonance condition of the Brillouin interaction. The model predicts how the acoustic wave, the signal amplitude and the gain spectral profile depend upon the pumping scheme. The analytical solution is an unprecedented tool to optimize the sensor configuration by determining the optimum pumping scheme.