cross-spectral matrix were computed across the sliding average of the edited EEG for all 19 leads for a total number of 81 and 1,539 log-transformed elements for each subject. The EEG values of each participant at each electrode were computed for each of the following frequency bands: delta (1–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–25 Hz), and gamma (30–40 Hz). Next, the following equation (1) was used to determine coherence62, 63:1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\begin{array}{rcl}{coherence}\,(\,{f}) & = & ({{\rm{\Sigma }}}_{{\rm{N}}}({\rm{a}}({\rm{x}}){\rm{u}}({\rm{y}})+{\rm{b}}({\rm{x}}){\rm{v}}({\rm{y}})){)}^{2}+({{\rm{\Sigma }}}_{{\rm{N}}}({\rm{a}}({\rm{x}}){\rm{v}}({\rm{y}})\\ & & +\,{\rm{b}}({\rm{x}}){\rm{u}}({\rm{y}})){)}^{2}/{{\rm{\Sigma }}}_{{\rm{N}}}({\rm{a}}({\rm{x}}{)}^{2}+{\rm{b}}({\rm{x}}{)}^{2}){{\rm{\Sigma }}}_{{\rm{N}}}({\rm{u}}({\rm{y}}{)}^{2}+{\rm{v}}({\rm{y}}{)}^{2})\end{array}$$\end{document}coherence(f)=(ΣN(a(x)u(y)+b(x)v(y)))2+(ΣN(a(x)v(y)+b(x)u(y)))2/ΣN(a(x)2+b(x)2)ΣN(u(y)2+v(y)2)anda(x) = cosine coefficent for the frequency (f ) for channel x b(x) = sine coefficent for the frequency (f ) for channel x u(y) = cosine coefficent for the frequency (f ) for channel y v(y) = sine coefficent for the frequency (f ) for channel y
