Energy-period distributions (yellow dots) of IMFs obtained with EMD from 2000 independent samples of synthetic noisy signals with α = 0 (the white noise), α = 0.5, α = 1 (flicker or the pink noise), α = 1.5, α = 2 (Brown(ian) or the red noise), and α = 2.5. Each sample contains 500 data points. All samples were normalised for their total energy to be unity. Period is measured in dimensionless evenly sampled time-steps between the data points. The energy averaged over each period is indicated by the red crosses. Blue lines represent the empirical dependence of the mean modal energy upon the period P, obtained with the linear fitting. Green lines show E_±(P) functions, the 99% and 1% confidence intervals, calculated for the chi-squared distribution given by Eq. (5). For the white noise (α = 0), the 99% confidence interval from Wu & Huang (2004), obtained as the second-order Taylor expansion of the exact dependence, is shown with the dashed lines.