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Chunk #15 — Methods — Eeg analyses: time–frequency decomposition

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Single-trial regression elucidates the role of prefrontal theta oscillations in response conflict.
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All analyses were performed in matlab. Single-trial data were first decomposed into their time–frequency representation by multiplying the power spectrum of the EEG (obtained from the fast-Fourier-transform) by the power spectrum of complex Morlet wavelets [ where t is time, f is frequency, which increased from 1 to 40 Hz in 30 logarithmically spaced steps, and σ defines the width of each frequency band, set according to 4/(2πf)], and then taking the inverse fast-Fourier-transform. From the resulting complex signal, an estimate of frequency band-specific power at each time point was defined as the squared magnitude of the result of the convolution Z (real[z(t)]2 + imag[z(t)]2), and an estimate of frequency band-specific phase at each time point was taken as the angle of the convolution result. Relatively long epochs were cut from the continuous EEG data (−1.5 to 2 s) to allow edge artifacts due to sudden transitions in signal values between trials to subside outside the window of interest. Taking long epochs and trimming edge artifacts is preferred over windowing, because the latter method attenuates real signal whereas the former