This low-pass-reduces-fast-signals lesson shows the same ideal low-pass rule after the input frequency rises above cutoff. With 6 Hz over a 3 Hz cutoff, the index is 2 and the squared response drops to 1/5 exactly only for the stated row. Real filters shift with component tolerances, source/load interaction, parasitics, finite active-device bandwidth, calibration limits, finite precision, and measurement uncertainty.
A first-order low-pass transmits less above cutoff. 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 signal is above the cutoff
With cutoff 3 hertz, the index is 2.
x=36=2
The low-pass squared ratio drops to one fifth
Budget 20 transmits only 4 through this low-pass stage.