Sensitivity analysis of time encoded bandlimited signals

A time encoding machine, consisting of a feedback loop containing an adder, an integrator and a Schmitt trigger, encodes amplitude information into a time sequence. We demonstrate how to construct a time decoding machine that perfectly recovers the amplitude information from the time sequence and is trigger parameter insensitive. We derive bounds on the error in signal recovery introduced by the quantization of the time sequence. We compare these with the recovery error introduced by the quantization of the amplitude of the bandlimited signal when irregular sampling is employed. Under Nyquist-type rate conditions, quantization of a bandlimited signal in the time and amplitude domains are shown to be largely equivalent methods of information representation.