Optimizing Weighting Factors for Multiple Window Spectrum Estimates
Marlon Almström · Lund University Publications Student Papers (Lund University) · 2021
Spectral estimation can be done using different techniques, where averaging the periodogram using multiple windows is one of the techniques. When using multiple windows, the spectral estimate is commonly obtained by having the windows for the subspectra equally weighted. The goal of this thesis is to find weights for the windows that give a better spectral estimate than the equally weighted spectral estimate. These weights are the resulting weights that minimizes the normalized mean square error, which is computed as an average within a certain frequency interval for two different spectral models and estimated from measured data. The optimized weights were computed for the Welch windows, the Thomson windows, the sinusoid windows, and the peak matched multiple windows. All of the windowed spectral estimates resulted in giving better spectral estimates when using the optimized weights. This was the case for both of the two spectral models that were used for the optimization of the weights. Examples of resulting time-varying spectra from measured Electroencephalogram data are shown.