A system with a high threshold takes longer to turn on than to turn off. If the input in A, plotted as a function of time, is delayed and smoothed by convolution with a boxcar function, the trace in B results. The delay from the rise in the input to the rise in the output is equal to that from the fall in the input to the fall in the output. However, if the system responds only when the output is above a high threshold (dashed line), the latency to response onset (ton) is longer than the latency to offset (toff) by an amount approximately equal to the time to rise to threshold. Thus, ΔAP approximates the integration time of the system in this simple demonstration.