the absolute value of which, termed coherence, is a measure of the phase coupling between signals at a given frequency. This can be seen by representing the complex-valued Fourier transforms in terms of their amplitudes Ai(f) and phases θi(f), i.e., Xi(f)= Ai(f) eιθi(f) and Xj(f)= Aj(f) eιθj(f), where ι denotes the imaginary unit. Using this notation, coherence has the following form:
