Most of the tasty stuff for impedance spectroscopy occurs above 500Hz sin waves. so you're pretty much not gonna have much luck with the sampling limited to 2kHz. Especially determining phase shift. I do wonder if we can do saw tooth or square wave excitation, to get at least an impedance. 1kHz impedance measurement (with out phase determination) is quite useful for battery testing.
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RE: Impedance Spectroscopy and Manual Control Sampling Rate