A system for amplifying a digital audio signal comprises a receiver 12 for receiving a digital audio signal, a level estimator 14 arranged to calculate the audio level of the digital audio signal, a gain control 16 arranged to receive a gain level, the gain level defining the desired amplification of the digital audio signal, a logic circuit 18 arranged to calculate the headspace in the digital audio signal and to divide the gain level into a scaling gain and an amplifier gain, the scaling gain not exceeding the calculated headspace, a digital signal processor 20 arranged to amplify the digital audio signal with the scaling gain, a digital-to-analogue converter 22 arranged to convert the amplified digital audio signal into an analogue signal, and an amplifier 24 arranged to amplify the analogue audio signal with the amplifier gain.