We will theoretically and experimentally study the effect of the linewidth and the frequency of a weak detuned signal on its amplified spectrum in the Brillouin amplifier. We will show that the spectral profile of the input signal is preserved during amplification only when the signal linewidth is much narrower than the Brillouin linewidth of the amplifier. If the signal linewidth is near or above the Brillouin linewidth, the frequency shift of the amplified signal with respect to the pump will be close to the Brillouin shift of the amplifier, and will be independent of the frequency shift of the input signal.