Common-offset cancellation by signal reversal ($S=(y_{+}-y_{-})/2,b=(y_{+}+y_{-})/2$)

If a controlled reversal changes the desired signal's sign while leaving an additive offset unchanged, readings $y_{+}=S+b$ and $y_{-}=-S+b$ separate them by half-difference and half-sum. Offset drift, gain changes, hysteresis or a background that also reverses violate the simple cancellation. Interleaving polarities and independent blank measurements test those assumptions; signal reversal does not cancel an arbitrary systematic error.