Slow Then Fast Cascade Uses Distinct Cutoffs - Electronic Circuits VII: Frequency Response and Filters Step by Step

The same signal can have different normalized indexes at different stages. 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 same signal is slow for the first cutoff

Against cutoff 12 hertz, the signal index is 1/2 and the ratio is 4/5.

x_1={6\over 12}={1\over 2}

The same signal is fast for the second cutoff

Against cutoff 3 hertz, the index is 2 and the final product is 4/25.

{4\over 5}\cdot {1\over 5}={4\over 25}