Analog signals can be fully encoded as an asynchronous time sequence generated by a time encoding machine (TEM). With knowledge of the parameters of the time encoding machine, the asynchronous time sequence can be decoded using a non-linear time decoding machine. In one embodiment, the non-linear time decoding machine generates a set of weighted Dirac delta functions centered in the intervals of the asynchronous time sequence of the time encoding machine output. The weighting of each of the delta functions is determined by the parameters of the TEM as well as the values of the time sequence. The generation of the series of delta functions is a nonlinear operation (500, 510, 520). The input signal can be recovered from the series of weighted delta functions by (530) applying this series through an impulse response filter.