# Power spectrum of uniform white noise

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 $$E[W_{i,j}] = \frac{a+b}{2}$$.