Magnetic field sensors and sensing methods are provided. A magnetic sensor module is configured to measure a magnetic field whose magnitude oscillates between a first extrema and a second extrema. The magnetic sensor module includes a magnetic sensor configured to generate measurement values in response to sensing the magnetic field, and a sensor circuit. The sensor circuit is configured to generate a measurement signal based on the measurement values, adjust an offset of the measurement signal according to an offset update algorithm and a first characteristic of the measurement signal, generate a pulsed output signal having pulses that are generated based on the adjusted measurement signal crossing the switching threshold, and selectively enable and disable the offset update algorithm based on a second characteristic of the measurement signal.