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Suppose $f$ is a signal of duration $t_d$ sampled each $0.01 sec$. After employing empirical mode decomposition (EMD) to $f$, $n$ number of intrinsic mode functions (IMF) would be extracted. Using Hilbert transform, instantaneous frequencies ($\omega$) and instantaneous amplitudes ($H$) were calculated. As a result the $\omega$ is a matrix with the number of rows equal to length of signal f and number of columns equal to $n$ (so is $H$). Now I want to construct marginal Hilbert spectrum using $\omega$ and $H$. I found the following formula in literature: $$h(\omega) = \int_0^{t_d} H(\omega,t)dt$$ What confuses me is that the result of integration is a vector of length n (that is the number of IMFs). On the other hand, the values of $\omega$ for each IMF differs from others and they are not increasingly sorted (like what we have in wavelet transform). I hope the above clearly explains my problem.

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