Low-Pass and High-Pass Complements

High-Pass Complements Low-Pass

fractions close

For the same first-order index, high-pass and low-pass squared ratios add to one. 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 high-pass keeps the same fast signal

At index 2, the high-pass squared ratio is 4/5.

∣H∣2=45|H|^2={4\over 5}
High-pass keeps fast signalThe high-pass ratio is checked.ffcratioinouthighpass

The two complementary fractions add to one

At the same index, the low-pass fraction is 1/5 and the high-pass fraction is 4/5.

15+45=1{1\over 5}+{4\over 5}=1
Low-pass complementThe low-pass fraction is the complement.ffcratioinoutlowpass