# Amplitude and frequency modulation detection of measured signal using Hilbert Transform.

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I presented a current signal from a dynamic eccentricity experiment on a switched reluctance motor (SRM) after FFT in the frequency domain (Hz). The orange graph shows the operation of the electric motor in a damaged condition (dynamic eccentricity), and the blue graph shows it in a correct operating condition.

I wanted to check whether amplitude (and phase) modulation occurs in the vicinity of the sixth harmonic (the sixth harmonic is a correct phenomenon resulting from the construction of the motor).

First, I filtered out the signal from the remaining harmonics (also eliminating the constant component)

To detect amplitude modulation, I decided to determine the envelope of the current signal using the Hilbert transform on the filtered signal. I determined the FFT from the absolute value of HT and the phase shift as a function of time.

In the third figure, two small harmonics can be seen in the damaged state. What do they mean? Do they say that these two harmonics participate in the modulation of the signal (analogously in a proper state, one harmonic?)? Interestingly, despite the lack of a constant component in the signal, it appears after the Hilbert transformation.

How do we interpret phase shift? From what I remember, there was something about the steepness of these runs.

This is a fragment of a code for Hilbert transform:

f=fs*((0:(L-1))/(L-1));

zero=zeros(1,L));

one=ones(1,L));

envelope=abs(hilbert(filtered_signal));

envelope1=abs(hilbert(filtered_signal1));

my_fft=abs(fft(envelope))/L;

my_fft1=abs(fft(envelope1))/L;

figure

plot3(f,zero,my_fft,f,one,my_fft1,'k')

and phase modulation

phase=detrend(unwrap(angle(hilbert(filtered_signal))));

phase1=detrend(unwrap(angle(hilbert(filtered_signal1))));

figure

plot3(t,zero,phase,t,one,phase1,'k')

I realize this is more of a scientific problem than a strictly programming one. Nevertheless, many people have similar issues, and I would be grateful for help explaining them.

##### 4 Comments

Mathieu NOE
on 21 May 2024

well, then if you have been through the litterature, what is the issue you're still facing ?

detecting the modulation presence is easy, interpreting and finding the relationship to each specific motor / drive possible damage cause is more challenging and requires a true in depth know how.

we don't even know what kind of motor / drive you are studying, nor what kind of damage you are dealing with.

hope some specialist could answer your question, but I think you are not asking in the right forum (IMHO)

god luck for the future

### Answers (1)

Joel Van Sickel
on 28 May 2024

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