Readout overlap is an interval check: a signal counts only when it shares positive time with the readout window. In this scan, the 6 to 10 signal overlaps the 4 to 11 window by 4 seconds, the 10 to 14 signal still has 1 second of overlap, and a signal starting at 11 only touches the endpoint and is rejected. Real timing gates also have jitter, detector latency, threshold choices, clock calibration, finite samples, and uncertainty.
Readout acceptance follows positive interval overlap, including endpoint rejection. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The first signal overlaps by four seconds
Signal interval 6 to 10 overlaps the window 4 to 11 by 4 seconds.
Δt=min(10,11)−max(6,4)=4
A narrow positive overlap still accepts
A later signal from 10 to 14 overlaps the same window by only 1 second, but the overlap is positive.
Δt=min(14,11)−max(10,4)=1
Touching the endpoint gives zero accepted overlap
A signal starting at 11 only touches the window endpoint at 11. Its overlap is 0, so it is rejected.