A simple spike train decoder inspired by the sampling theorem

Reconstructing a time-varying stimulus estimate from a spike train (Bialek's "decoding" of a spike train) has become an important way to study neural information processing. In this paper, we describe a simple method for reconstructing a time-varying current injection signal from the simulated spike train it produces. This technique extracts most of the information from the spike train, provided that the input signal is appropriately matched to the spike generator. To conceptualize this matching, we consider spikes as instantaneous "samples" of the somatic current. The Sampling Theorem is then applicable, and it suggests that the bandwidth of the injected signal not exceed half the spike generator's average firing rate. The average firing rate, in turn, depends on the amplitude range and DC bias of the injected signal. We hypothesize that nature faces similar problems and constraints when transmitting a time-varying waveform from the soma of one neuron to the dendrite of the postsynaptic cell.