Finite dot-product bins are scanned across reviewed basis roles. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
A bin is still product-and-sum arithmetic
The alternating source multiplies sample by basis point by point. The dot sum is the visible finite bin value.
1+1+1+1=4
Changing the basis changes what the same samples show
The same alternating samples have zero dc sum but four alternating sum. The first row shows the dc basis on a flat signal.