From Nyquist plot to real conductivity spectra (sigma)

[Olha]

TL;DR

From Nyquist plot to real conductivity spectra (sigma) vs frequency

Hi, I have data of impedance but due to limitation of software after measurement I do not receive numerical values for admittance and real conductivity vs frequency. How mathematically I can convert Nyquist plot into plot real conductivity vs frequency?

 

[Gordianus]

Your plot already shows the real part of the complex conductivity. Do you need the imaginary part?

 

[Olha]

The image is the result I want to get. For now I have Nyquist plot Im vs Re, which I would like to transform it to the plot you see attached, real part of complex conductivity vs frequency. I have done it trough admittance but I am not sure in all formulas I used for it...

 

[Gordianus]

Please, show us your method.