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Given a white noise image $W_{i,j} \sim U[a,b]$ where each pixel is distributed uniformly in $[a,b]$, how would I go about computing its power spectral density? That is, I want to find $E[|\hat{W}_{i,j}|^2]$. Am I supposed to write it out through the autocorrelation function and then use the fact that pixels are independent of each other to split the expectation? Would this just yield a non-zero term at the DC? That is, the squared mean grey value $E[W_{i,j}] = \frac{a+b}{2}$.

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The fourier transform of the two dimensional autocorrelation function should do it.

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