The output would be the derivative ("instantaneous rate of change") of the input current so it's only passing an AC signal (the variations decomposed into all its harmonic frequencies).A varying DC to a transformer can induce a flux that can be used to get a varying dc at the other end of the transformer that depends on the turns ratio hence dc transformer
Mathematically, this is another example of calculus in action. Because the voltage is proportional to the flux’s rate-of-change, we say that the voltage waveform is the derivative of the flux waveform, “derivative” being that calculus operation defining one mathematical function (waveform) in terms of the rate-of-change of another. If we take the opposite perspective, though, and relate the original waveform to its derivative, we may call the original waveform the integral of the derivative waveform. In this case, the voltage waveform is the derivative of the flux waveform, and the flux waveform is the integral of the voltage waveform.