Time encoding machines with multiplicative coupling, feedforward, and feedback

We introduce a novel class of time encoding machines (TEMs) that exhibit multiplicative coupling, and, feedforward and feedback. We show that a machine with multiplicative coupling is I/O equivalent with an integrate-and-fire neuron with a variable threshold sequence. The same result holds for a TEM with feedforward while a machine with,feedback is I/O equivalent with an asynchronous sigma/delta modulator with variable thresholds. For all TEMs, an input band-limited signal can be perfectly recovered from the zero crossings of the modulated signal and the threshold sequence. We present the optimal decoding algorithm and give conditions for perfect signal recovery.