If it is an + square wave just add a diode and a cap. If it is an AC square wave add a bridge rectifier and a smaller cap.
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LVDTs NEED sinewave excitation if you want a chance of linear outputs. The standard methods usually use a phase-sensitive detector, but Analog Devices do the AD598, which does the excitation and demodulation for you.
The linear variable differential transformer generates a voltage proportional to displacement of an iron rod this makes the device a great electronic measuring stick for motion like a water tank or a plant growth or a sub conscious smile. A