# How to plot the Hilbert Spectrum in Hilbert-Huang transform?

I'm working on integral transforms for a science initiation project and i got to do a work on the Hilbert-Huang transform.

I've seen on the internet that, after one found the IMFs with the EMD method, you can do a Hilbert Spectrum plot of the absolute value of the componentes $H(\omega,t)$ where $t$ is for time, and $\omega(t)$ is the instantaneous frequency.

Suppose i got 5 IMFs stored in 5 vectors in GNU/Octave (or Matlab, wharever). How can i do such plot?

• after applying hilbert transform and getting time-frequency plot(like in plot_hht function)how to plot a 3D figure amplitude-time-frequency ,I saw it in an article and don't know how they do it....any ideas???..thank you – user15760 May 9 '15 at 7:10

## 1 Answer

Final step is pretty straightforward. All you need to do is to apply the Hilbert Transform to each IMF and extract the instantaneous frequency from analytical signal. Instantaneous frequency is given by: $$\omega(t)=\dfrac{d\phi(t)}{dt}$$ where $\phi(t)=\mathrm{arg}[x_a(t)]$ (unwrapped phase of the analytical signal). Keep in mind that MATLAB (Octave) hilbert function already returns analytical signal.

In fact you might want to re-use this code from Mathworks File Exchange: plot_hht it is a good starting point.

• Thanks for the answer! I know how to compute the instantaneous frequency, but i want to know how exactly do i do the 2d plot. But i will take a look at that code, thanks a lot! :) – ebernardes Feb 3 '15 at 12:42
• This is a question would the Hilbert-Huang transform be appropriate for non stationary time series as I have read books where this is hinted I could not find a definitive answer – Barnaby Feb 3 '15 at 13:59
• Both for non-stationary and non-linear. – jojek Feb 3 '15 at 15:47