Finite Bin Role Three-Row Scan - Signals and Noise in Physics Measurements Step by Step

Reviewed finite basis roles are scanned by exact dot products. 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 dc basis adds all samples

With basis all ones, the dot sum is ten.

1+2+3+4=10

The alternating basis cancels this ramp

The same samples can give a negative dot when the basis signs alternate.

1\mathbin{-}2+3\mathbin{-}4=\mathbin{-}2

A third reviewed basis gives its own finite dot

The table compares three checked roles on the same sample row.

\begin{array}{c|c}\text{role}&\text{dot}\\\text{dc}&10\\\text{alternating}&\mathbin{-}2\\\text{two-cycle}&\mathbin{-}4\\\end{array}