Filter Windows and Gain Budgets

Filter Chain Audit Closes the Budget

every stage checked

The capstone multiplies window ratios and gain-squared scaling in one checked chain. 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 passive window closes before gain

Input budget 25 becomes passive output 16 after the high-pass and low-pass stages.

25⋅45⋅45=1625\cdot {4\over 5}\cdot {4\over 5}=16
Passive auditThe passive output is recorded separately.ffcratioinoutffcratioinoutratioinouthighpasslowpassgain

The final post-gain budget is the full product

Gain 2 gives gain-squared 4 and final budget 64.

25⋅45⋅45⋅22=6425\cdot {4\over 5}\cdot {4\over 5}\cdot 2^2=64
Full filter auditEvery displayed stage and final budget is checked.ffcratioinoutffcratioinoutratioinouthighpasslowpassgain