Average of the power spectrum of Poisson noise

[arcTomato]

TL;DR

Poisson distribution

I am learning about noise that follows a Poisson distribution. When I do a Fourier transform of the data with only Poisson noise to get the power spectrum, what is the average value of the power spectrum?

 

[marcusl]

You can find it by using the Fourier energy theorem (often called Plancherel's or Parseval's theorem).