Hilbert–Huang transform: Instantaneous frequency

Question

I'm implementing the "Empirical Mode Decomposition" in Java. The next step is Hilbert–Huang transform and I need to find how to get the "Instantaneous frequency". Does someone Know how to get it?

Using the EMD method, any complicated data set can be decomposed into a finite and often small number of components, which is a collection of intrinsic mode functions (IMF). Next step is Hilbert–Huang transform. From this I calculate the signal's phase and after I must calculate the instantaneous frequency, I search in Matlab code like in this link: http://read.pudn.com/downloads100/sourcecode/math/408870/emd/instfreq/archive/ifreq.m__.htm

but I don't understand it.

Thanks

Please elaborate on what you want to achieve and what you have tried to get there. — Jeroen Kransen, Apr 28 '14 at 18:18
are you willing to share your java code so others can benefit from it's implementation? — angryip, Aug 13 '17 at 12:01

score 1 · Answer 1 · answered Oct 27 '17 at 17:26

1

The instance frequency can be calculated in Python by

def hilb(s, unwrap=False):
    from scipy.signal import hilbert
    H = hilbert(s)
    amp = np.abs(H)
    phase = np.arctan2(H.imag, H.real)
    if unwrap: phase = np.unwrap(phase)
    return amp, phase

inst_amp, phase = hilb(imf, unwrap=True)
inst_freq = np.diff(phase)

answered Oct 27 '17 at 17:26

Annie Liang li

11
1

Why this answer is not selected as best? – Emil Nov 26 '19 at 10:16
Hi, I was using your code but getting nan values in hilbert(s), what can be the issue? – poshita singh Feb 24 '20 at 06:57

score 0 · Answer 2 · answered Jan 18 '16 at 18:03

The Hilbert-Huang transform is the combination of empirical mode decomposition (EMD) and Hilbert transform.

First, EMD is an algorithm that gives you the intrinsic mode functions (IMFs).

The Hilbert transform is then applied to each of the IMFs.

From an IMF, the Hilbert transform gives a pi/2 phase delayed signal from which you can compute the phase, and the time-derivative of the phase, which is proportional to the instantaneous frequency.

You will find interesting tutorials and details about the algorithmic variations of EMD on that page: http://perso.ens-lyon.fr/patrick.flandrin/emd.html

score 0 · Answer 3 · answered Jun 27 '19 at 07:35

You can process your signal data using Hilbert-Huang Transform (HHT) which is the combination of Empirical Mode Decomposition (EMD) and Hilbert Spectrum Analysis (HSA) with Matlab or Python. In Matlab or Python, there is the HHT method that you can use directly and do not need to calculate the Instantaneous Frequency (IF) by yourself.

For example with Matlab:

First, you can get IMF and residual by implementing emd to signal data, the code is: [IMF,residual,info] = emd(signal,'Interpolation','pchip', 'Display', 0);

Then, the IF, that is IMFINSF, can be obtained by hht(IMF, fs) in which fs is the sample frequency [P,F,T,IMFINSF,IMFINSE]=hht(IMF,fs);

In addition, there are also some tools and methods in Python.

Can you share the python tools. – poshita singh Feb 24 '20 at 08:03 — poshita singh, Feb 24 '20 at 08:03

Hilbert–Huang transform: Instantaneous frequency

3 Answers3