Filter Source-Factor Depth Scans

Input Budget Three-Row Scan

Three source-budget rows separate input size from a fixed cutoff ratio. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Ten input units halve to five output units

At cutoff, the ratio is fixed at 1/2. Input budget 10 becomes output budget 5.

10⋅12=510\cdot {1\over 2}=5
Ten-budget low-pass rowOnly the input budget changed.ffcratioinoutlowpass

Twenty input units halve to ten output units

The middle row uses input budget 20 with the same cutoff ratio. Output is 10.

20⋅12=1020\cdot {1\over 2}=10
Twenty-budget low-pass rowThe output bar scales with the source budget.ffcratioinoutlowpass

Thirty input units halve to fifteen output units

The final source row raises input budget to 30. The same exact ratio gives 15 output units.

30⋅12=1530\cdot {1\over 2}=15
Thirty-budget low-pass rowThree rows separate input size from filter ratio.ffcratioinoutlowpass