This low-pass-keeps-slow-signals lesson uses an ideal first-order low-pass model to show that a below-cutoff signal keeps most of its squared budget. The 6 Hz signal against a 12 Hz cutoff gives index 1/2 and a 4/5 squared ratio only for the stated model row. Real filters add component tolerances, loading, parasitic capacitance and inductance, finite bandwidth, calibration limits, finite precision, and measurement uncertainty.
A first-order low-pass transmits most of a below-cutoff squared budget. 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 below the cutoff
The same 6 hertz signal compared to a 12 hertz cutoff has index 1/2.
x=21
The low-pass squared ratio is four fifths
The low-pass ratio is 4/5, so budget 20 becomes 16.