Consider the problem of continuously estimating the power spectrum from a sequence x(n) based on averaging periodograms with exponential weighting into the past. Thus with , we have
where successive periodograms are assumed to be uncorrelated and w is the (expo-nential) weighting factor.
(a) Determine the mean and variance of for a Gaussian random process.
(b) Repeat the analysis of part (a) for the case in which the modified periodogram defined by Welch is used in the averaging with no overlap.
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