Optimizing Weighting Factors for Multiple Window Spectrum Estimates
(2021) In Bachelor’s Theses in Mathematical Sciences MASK11 20202Mathematical Statistics
 Abstract (Swedish)
 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... (More)  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 timevarying spectra from measured Electroencephalogram data are shown. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/studentpapers/record/9040355
 author
 Almström, Marlon ^{LU}
 supervisor

 Maria Sandsten ^{LU}
 organization
 course
 MASK11 20202
 year
 2021
 type
 M2  Bachelor Degree
 subject
 publication/series
 Bachelor’s Theses in Mathematical Sciences
 report number
 LUNFMS40492021
 ISSN
 16546229
 other publication id
 2021:K5
 language
 English
 id
 9040355
 date added to LUP
 20210512 09:45:00
 date last changed
 20210603 15:54:26
@misc{9040355, abstract = {{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 timevarying spectra from measured Electroencephalogram data are shown.}}, author = {{Almström, Marlon}}, issn = {{16546229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor’s Theses in Mathematical Sciences}}, title = {{Optimizing Weighting Factors for Multiple Window Spectrum Estimates}}, year = {{2021}}, }