A record of samples of stationary white noise is Fourier transformed

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Scientific Computing for Physicists, Ch Spectra with error bars: the fast transform, convolution and spectral estimation

Problem

A record of N=8192N = 8192 samples of stationary white noise is Fourier transformed, giving a periodogram S^k\hat{S}_k at each of the interior bins (N/2−1N/2 - 1 of them, excluding the zero and Nyquist bins). Each ordinate, normalised so the true noise level is SS, obeys P(S^k>aS)=e−aP(\hat{S}_k > aS) = e^{-a}. ((a)) Compute the probability that a single noise bin exceeds four times the true level. ((b)) Estimate how many of the interior bins are expected to exceed this threshold by chance alone.

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