1. An asynchronous pulse processing (APP) apparatus comprising: an apparatus gain block configured to scale an input signal by a first scale value to produce a scaled input signal; an apparatus summation block configured to produce a composite signal, the composite signal representing the scaled input signal minus an input summation signal multiplied by a reverberation signal, minus the reverberation signal scaled by a second scale value, and plus a function-modified feedback signal; an integrator configured to integrate the composite signal and to produce an integrated composite signal; and a time encoder configured to time-encode the integrated composite signal and produce the reverberation signal, wherein the input summation signal represents the input signal summed with a reverberation inhibition signal.