A magnetic field sensor includes at least one magnetic field sensing element configured to generate a magnetic field signal indicative of a magnetic field associated with a target, an analog-to-digital converter configured to convert the magnetic field signal into a digital magnetic field signal, and a controller responsive to the digital magnetic field signal and configured to adjust an offset of the digital magnetic field signal during a first operational phase and to increase a gain of the digital magnetic field signal during a second operational phase following the first operational phase. The first and second operational phases occur during a running mode of sensor operation.