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- 24
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