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# proefschrift gommer inhoud met kaft.indd

Chapter 2
Table 1. Summary of parameter choices in transfer function estimation.
Combina- Detrend- Window Window Triangular Smoothing
tion ing length duration smoothing bandwidth
samples s window Hz
width
Mean
I subtrac- 256 51.2 3 0.04
tion
Smooth-
II 256 51.2 3 0.04
ness priors
Mean
III subtrac- 2048 409.6 31 0.04
tion
Smooth-
IV 2048 409.6 31 0.04
ness priors
To reduce variance of the spectral estimates of the transfer function either spec-
tral averaging or spectral smoothing can be performed. Spectral averaging was
first introduced by Welch 32 and averaged spectra were calculated over multiple
half overlapping epochs. An epoch length of 50 seconds is chosen to result in an
adequate frequency resolution of at most 0.02 Hz. Spectral smoothing reduces
variance by filtering the spectrum with a triangular window averaging over a
frequency band. In this case the spectrum is calculated over almost the entire
measurement resulting in a much finer frequency resolution. In this study four
different combinations of parameter settings (table 1) for detrending were tested.
In method I and III only mean subtraction was performed, whereas in method II
and IV smoothness priors detrending 29 with a 0.04 Hz cut-off frequency
!"=500) was used to remove very low frequency trends. Each data epoch was
windowed with a Hanning-window. In method I and II half overlapping 51.2 s
long epochs of 256 data points with a 5 Hz resampling rate were used; in method
III and IV 2048 points, corresponding to a 409.6 s epoch length. In method I and
II the spectrum was smoothed with a 3-point triangular moving average window
corresponding to a full width half max bandwidth of 0.04 Hz; in III and IV a 31
points wide triangular window, also corresponding to a bandwidth of 0.04 Hz
18, 31.
From the resulting transfer functions, mean coherence, phase and gain were
calculated in the 0.04-0.16 Hz frequency range. The 0.04 Hz lower border has
been chosen because the limited duration of the recordings makes interpretation
of results below this frequency difficult. The upper frequency is chosen to in-
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