Spike timing-dependent plasticity, related to differential Hebb-rules, has become a leading paradigm in neuronal learning, because weights can grow or shrink depending on the timing of pre- and post-synaptic signals. Here we use this paradigm to reduce unwanted (acoustic) noise. Our system relies on heterosynaptic differential Hebbian learning and we show that it can efficiently eliminate noise by up to -140 dB in multi-microphone setups under various conditions. The system quickly learns, most often within a few seconds, and it is robust with respect to different geometrical microphone configurations, too. Hence, this theoretical study demonstrates that it is possible to successfully transfer differential Hebbian learning, derived from the neurosciences, into a technical domain.