How to get the phase in function of time of the hht (Hilbert-H​uang-trans​form?

Hi,

we try to decompensate a signal with matlab with a emd (empirical mode decomposition) and with hht(Hilbert-Huang transform). From the IMFs, we try to compute the instantaneous phase IP. It is already possible with python:

https://emd.readthedocs.io/en/stable/emd_tutorials/00_quick_start/emd_tutorial_00_start_01_quicksift.html

IP, IF, IA = emd.spectra.frequency_transform(imf, sample_rate, 'hilbert')

Is it also possible with matlab? I have only found this article about emd: https://de.mathworks.com/help/signal/ref/emd.html

Thanks for your help.

Answer 1

[AH]

Instantaneous phase can be obtained by taking the integral from the instantaneous frequency, where is the initial phase at time and is the instantaneous frequency. To compute the integral numerically, cumtrapz can be used.

load('sinusoidalSignalExampleData.mat','X','fs')
t = (0:length(X)-1)/fs;
[imf,residual,info] = emd(X,'Interpolation','pchip');
iph = cumtrapz(t,imf);
figure
subplot(211),plot(t,imf(:,3)),xlabel("Time [sec]"),ylabel("Inst. Freq."),grid("minor")
subplot(212),plot(t,iph(:,3)),,xlabel("Time [sec]"),ylabel("Inst. Phase."),grid("minor")

[thomas baranowski]

Hi, thank you. This makes senses. I am just wondering why I get different results with matlab using:

[imf,residual,info] = emd(X,'Interpolation','pchip');

iph = cumtrapz(t,imf);

and python using: IP, IF, IA = emd.spectra.frequency_transform(imf,sample_rate,'nht',smooth_freq=3).

If I use matlab i get imf 4 as and in python imf5 as 7-8khz signal, which we like to use. Also the phase looks totaly different at python and matlab.

[thomas baranowski]

[thomas baranowski]

Here are is the signal and time files.

Best Regards