# LUP Student Papers

## LUND UNIVERSITY LIBRARIES

### Optimizing Weighting Factors for Multiple Window Spectrum Estimates

(2021) In Bachelor’s Theses in Mathematical Sciences MASK11 20202
Mathematical 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)
author
supervisor
organization
course
year
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
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}},
}

```