Guaranteed Reconstruction from Integrate-and-Fire Neurons with Alpha Synaptic Activation

Time encoding of continuous time signals is an alternative to classical sampling paradigms. The signal is encoded in the timing of output samples rather than their amplitudes. Of particular interest are integrate-and-fire time encoding machines (IF-TEM) for sampling signals with finite rate of innovation (FRI). In contrast to state-of-the-art methods we propose an IF-TEM where we employ a biologically inspired and smooth sampling kernel, the alpha synaptic function, and show that perfect reconstruction can be achieved using this kernel. Furthermore, we derive conditions on the input signal, a train of scaled Diracs, such that not only can we guarantee the generation of useful samples, even when the Diracs have arbitrary sign, but also that these useful samples can be determined from amongst the non-useful samples. Thus, reconstruction of signals satisfying these conditions is always possible.