Averaging Gate Budget Cross-Scan - Signals and Noise in Physics Measurements Step by Step

The gate is a residual-budget check, not just an average label. With target 10 and limit 4 held fixed, the squared residual budget grows from 0 to 8 and the last row is rejected; real averaging gates must account for calibration, baseline noise, finite samples, gate width, and uncertainty.

A finite residual budget is scanned across wider readings. 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 gate uses squared residuals

The checked source has target ten and limit four. Its accepted bit comes from the residual budget, not from the average alone.

(-1)^{2}+1^{2}=2

A wider run can cross the same gate limit

The target and limit stay fixed. The squared budget grows from zero to eight, so the last row is rejected.

\begin{array}{c|c|c|c}\text{readings}&\text{budget}&\text{limit}&\text{accepted}\\\left(10,10,10,10\right)&0&4&1\\\left(9,11,10,10\right)&2&4&1\\\left(8,12,10,10\right)&8&4&0\\\end{array}