Graduate Average of the power spectrum of Poisson noise

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The discussion centers on understanding the average value of the power spectrum derived from Poisson noise through Fourier transforms. It highlights the application of the Fourier energy theorem, also known as Plancherel's or Parseval's theorem, to calculate this average. Participants emphasize that the power spectrum of Poisson noise is proportional to the mean of the noise, which is a key aspect of its statistical properties. The conversation also touches on the implications of these findings in various fields, such as signal processing and statistical analysis. Overall, the average value of the power spectrum for Poisson noise can be effectively determined using established mathematical principles.
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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?
 
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You can find it by using the Fourier energy theorem (often called Plancherel's or Parseval's theorem).
 

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