Thank you and duly noted, however I havn't been able to measure any DC current using the shunt resistor method. Also it is my understanding that after integrating the output voltage, it has to be scaled by a factor of 1/M, where M is the mutual inductance between the coil and wire being measured.The coil will not respond to the constant (DC) part of the current being measured. So the coil output will be an AC voltage and the current being measured will be the integral of this voltage with the DC part removed, also AC. You may want to "add in" the DC via analysis of the circuit or a different DC current measurement.
What do you mean by "true wave shape"? the instantaneous current?In any case if you perform an absolute value you will distort the true wave shape (rectification). I suppose you may want to do that, but I doubt it.
Thank you and duly noted. So when would I not use the absolute value? I mean if the instantaneous current is 1/M∫abs(voltage)?If you are using the result to calculate power then yes use he absolute value.
More specifically for power you want to integrate the product of the instantaneous Voltage and instantaneous Current.
If the voltage is constant you can take that outside the integral. Eg integrate the absolute current then multiply by the voltage.