The filter-chain audit closes the whole budget by multiplying the high-pass ratio, low-pass ratio, and gain squared in one checked product. Input budget 25 times 4/5 times 4/5 times gain-squared 4 equals 64 exactly for the stated ideal stages; real chains add component tolerance, stage loading, op-amp bandwidth, phase, source and load impedance, noise, temperature drift, and measurement uncertainty.
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.