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We have developed and tested a novel artificial neural network for the processing of temporal signals. The working of the units (TempUnit) is based on the mechanism of temporal summation as observed in biological neurons. Contrary to traditional neural networks, the TempUnit optimizes its basis function by supervised learning. The model was tested on cortical and associated muscular (EMG) recordings from the behaving primate. The TempUnit showed a 2.3 times better performance in mapping spiking to EMG activity than a time delay multi-layer perceptron. The TempUnit model demonstrated correct capacities for inverse computation. Indeed, we calculated biologically compatible activities for 3 cortical neurons from EMG recordings. Data compression capacity of the TempUnit was tested on audio data and compared to the MP3 compression standard. For a similar reproduction quality, we found a compression rate 5 times higher than in MP3.