Hi there,
Im pretty sure a square wave pulse works too, but you can't just connect
the output of a signal generator to the coil and expect to get the right
wave in most cases because the signal generator output impedance
characteristic will affect the overall waveform seen during and after
the pulse. A diode also has to be incorporated, between the signal
generator and the coil, so that when the sig gen wave goes low
the coil gets totally disconnected from the sig gen output.
Of course a relay would work too.
Probably have to use some damping too, like a 100k resistor or
something like that to prevent extremely high voltage spikes
from damaging the test equipment.
Just some ideas.
Of course another way is to use a sweeping sine wave
and look at the current response.