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 time-varying spectra from measured Electroencephalogram data are shown. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/student-papers/record/9040355
- author
- Almström, Marlon LU
- supervisor
- organization
- course
- MASK11 20202
- year
- 2021
- type
- M2 - Bachelor Degree
- subject
- publication/series
- Bachelor’s Theses in Mathematical Sciences
- report number
- LUNFMS-4049-2021
- ISSN
- 1654-6229
- other publication id
- 2021:K5
- language
- English
- id
- 9040355
- date added to LUP
- 2021-05-12 09:45:00
- date last changed
- 2021-06-03 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 time-varying spectra from measured Electroencephalogram data are shown.}}, author = {{Almström, Marlon}}, issn = {{1654-6229}}, language = {{eng}}, note = {{Student Paper}}, series = {{Bachelor’s Theses in Mathematical Sciences}}, title = {{Optimizing Weighting Factors for Multiple Window Spectrum Estimates}}, year = {{2021}}, }