There is described a sensor comprising an excitation winding, a signal generator operable to generate an excitation signal and arranged to apply the generated excitation signal to the excitation winding, a sensor winding electromagnetically coupled to the excitation winding and a signal processor operable to process a periodic electric signal generated in the sensor winding when the excitation signal is applied to the excitation winding by the signal generator to determine a value of a sensed parameter. The excitation signal comprises a periodic carrier signal having a first frequency modulated by a periodic modulation signal having a second frequency, the first frequency being greater than the second frequency. In this way, the sensor is well suited to using digital processing techniques both to generate the excitation signal and to process the signal induced in the sensor windings. In an embodiment, the sensor is used to detect the relative position of two members. In other embodiments, the sensor is used to detect environmental factors such as temperature and humidity.