The same sample row can look different when it is folded against different finite-bin basis roles. The diagram labels the samples, basis, dot sum, and role together so the bin name has to match the arithmetic instead of acting like a caption.
The dc role gives 1+2+3+4 = 10, the alternating role gives 1-2+3-4 = -2, and the two-cycle role gives -4 for the stated toy samples. Real measurements still carry bin-edge placement, sample timing, baseline, and quantization uncertainty.
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.
1−2+3−4=−2
A third reviewed basis gives its own finite dot
The table compares three checked roles on the same sample row.