# How to shift an AGN X-ray spectrum to rest frame

I have limited information to shift a spectrum (in the X-ray 0.5-10 keV bandpass) from redshift $$z=2$$ to the rest frame. I have a plot of normalized (photon) counts s$$^{−1}$$ keV$$^{−1}$$ as a function of energy (keV). Is there a way to shift the spectrum I have to rest frame? Or do I really need luminosity distance, etc.?

• How ... from Your question title is unclear. Can you edit?
– user1569
Jul 8 '17 at 14:48
• I tried to make some edits to make your question more clear. Feel free to rollback if you feel I mis-interpreted your question. Jan 15 at 14:10

The frequency is related to the redshift by $$\frac{\nu_{\rm obs}}{\nu_{\rm emit}} = \frac{1}{1+z}$$
$$\frac{I_{\nu}}{\nu^3} = {\rm constant}$$
where $I_{\nu}$ is the specific radiative intensity.
The specific count rate (counts per area per time per energy interval) is proportional to $I_{\nu}/\nu$. (Do you see why?)
That should give you enough information to derive how the measured count rate changes with $z.$ Of course, to know the actual value, not just the function of $z$, you'd need to know the actual count rate measured, not just the normalized value.