Why would a sensor output an inverted signal?
If you are describing an encoder - not a sensor then your outputs are probably:

X+: 0 and 5V. (not ± 5 V)
X-: X+ inverted.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. A typical A-B-Z quadrature encoder output waveform with differential outputs.

The inverted output gives the ability to improve noise immunity in the presence of electrical noise.



Figure 2. This diagram illustrates how a differential encoder is able to ignore noise. Channel Ā is the inverse of channel A, generated inside the encoder. However, when noise is introduced along the wire between the encoder and the encoder interface, the noise will be almost identical on both channels. Since the noise is not inverted on channel Ā, the differential encoder interface can perform a few simple operations to filter out the noise. Source: Phidgets.