Three signal-frequency rows show low-pass output falling as the source moves 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

Zero hertz is fully inside a low-pass

With cutoff 6 hertz, a 0 hertz signal has low-pass ratio 1. Output budget stays 20.

201=2020\cdot 1=20
Zero-frequency low-pass rowThe frequency marker starts at zero while the cutoff stays fixed.ffcratioinoutlowpass

At cutoff the low-pass keeps one half

The signal rises to 6 hertz, equal to cutoff. The exact squared ratio is 1/2, so output budget is 10.

2012=1020\cdot {1\over 2}=10
Cutoff low-pass rowThe same source budget is halved at cutoff.ffcratioinoutlowpass

Twelve hertz is above cutoff and mostly rejected

At 12 hertz against the same cutoff, the ratio is 1/5. Output budget falls to 4.

2015=420\cdot {1\over 5}=4
Fast low-pass rowThree source-frequency rows show the low-pass slope.ffcratioinoutlowpass