Locally smoothing the periodogram yields one of the most successful methods for non-parametric spectral estimation. Nevertheless, no much guideline was available for choosing the window parameters and span for smoothing. Here we derive the window parameters and span that minimize an asymptotically unbiased estimate of the spectral estimation error variance. The so-obtained optimally smoothed periodogram is shown to outperform the commonly used uniformly smoothed periodogram. Furthermore, a technique is presented where the window parameters are chosen separately for each of a number of different frequency bands. This technique reduces the variance of the spectral estimates even further, at the price of an increased computational complexity.
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