Filter Ratio Cross Scans

High-Pass Complement Three-Row Scan

the same cutoffs reverse

The same frequency/cutoff rows show the high-pass complement without decimals. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

At cutoff the high-pass also keeps one half

The same cutoff row gives high-pass ratio 1/2 and output budget 10.

20⋅12=1020\cdot {1\over 2}=10
High-pass scan rowAt cutoff the high-pass squared budget also halves.ffcratioinouthighpass

A higher cutoff blocks this low-index signal

With cutoff 12 hertz, the high-pass ratio is only 1/5. The output budget is 4.

20⋅15=420\cdot {1\over 5}=4
High-pass scan rowBelow cutoff, the high-pass budget is small.ffcratioinouthighpass

A lower cutoff passes the same signal

With cutoff 3 hertz, the high-pass ratio is 4/5. The output budget is 16.

20⋅45=1620\cdot {4\over 5}=16
High-pass scan rowThe high-pass scan complements the low-pass scan.ffcratioinouthighpass