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Oscillations about the mean trends and their energy history. Xk(t) is the kth-order oscillations about the kth-order trend of the MBP, Mk(t)MBP (see Eqs. 4 and 8). The Hilbert spectrum of Xk(t) was computed. An integration of the square of the Hilbert amplitude spectrum over all frequencies yields the energy of oscillations (EO). EO(t) corresponding to Xk(t) is denoted by Ek(t). (Upper) Xk(t) (k = 6, 8, 9, … 12) and Ek(t) (k = 6, 8, 9). (Lower) X6(t) and E6(t) at a larger scale.
