How to find peaks of the given signal and find the phase shift with respect to the Oscillator 1 signal?

I have this set of 8 signals, I am trying to find the peaks of each signal with respect to time and also I want to find the phase shift of Oscillator 2 to Oscillator 8 with respect to Oscillator 1 signal. Thanks in advance.

I have also attached the Data.mat file.

[Jay Vaidya]

I have progressed that I can find the peaks of each signal by using

[pks,locs,widths,proms] = findpeaks(data(i,:),data(1,:),'MinPeakHeight',1.7)

But then every signal has different length vector for peaks. I don't understand if I can use sampling here.

[KSSV]

Check this, it might be useful.

https://in.mathworks.com/matlabcentral/answers/439172-how-to-determine-the-phase-difference-phase-shift-between-two-signals

Answer 1

[Bjorn Gustavsson]

If you had regularly sampled data (it doesn't seem so) this would best be done with spectrogram. That would give you the spectrogram of the function (i.e. the short-time-Fourier-transform). From that you should take the angle of the fundamental component as the phase-shift between the signals. In principal you could do it with the regular fft as well, but your signal seems to be a bit varying with time.

However, you might have to address the time-variation of your sampling first.

Otherwise this is how I'd do it:

[S1,F1,T1] = spectrogram(data(2,:),hanning(1024),216,[],Fs);
[S2,F2,T2] = spectrogram(data(3,:),hanning(1024),216,[],Fs);
subplot(3,1,1)
pcolor(T1,F1,log10(abs(S1))),shading flat
subplot(3,1,2)
pcolor(T2,F2,log10(abs(S2))),shading flat
subplot(3,1,2)
pcolor(T1,F1,angle(S1.*conj(S2))),shading flat

From that you'd have to start to identify the fundamental frequency of your signals, and then take the corresponding phase-shift.

HTH

[Jay Vaidya]

Okay let me try this. Though, just to tell you that I do have the FFT data of all these signals. These are the signals generated by a electronic simulator and I got the FFT data of these signals too. I can change the time duration for which I want the FFT data too. Below is the FFT data snapshot. Can I use it by any means? It gives the fundamental frequency and the harmonics

This is the new time domain data and the figure. Data file is attached too.

[Bjorn Gustavsson]

You need to do a couple of things before you get to your answer. First, before you get to any type of Fourier-transforming you need to look at your sample-times (I'll have to assume that is the first row of your data):

figure
subplot(3,1,1)    
plot(data(1,:))
subplot(3,1,3)
hist(data(1,:),200)
hist(diff(data(1,:)),200)
hist(diff(data(1,:)),100)
hist(diff(data(1,:)),200)
subplot(3,1,2)
plot(diff(data(1,:)))                  
plot(diff(data(1,:)),'.')

So there you see that you have unevenly sample-intervalls. That's one task to resolve.

Then we should have a closer look at the signals (always look at the signal before analysing away):

figure
subplot(2,1,1)
plot(data(1,:),data(2:3,:))
subplot(2,1,2)
plot(data(1,:),data([2,4],:))

If you zoom in on the beginning of these plots, you'll notice that there is an "onset-time" of ~2e-5 time-units. Then you'll see that there is some change of the shift between the signals around 3e-4 - 4.5e-4 time-units.

Since you don't have regularly sampled time-series you cannot use fft-analysis straight off, but since you seem to have sufficiently high sampling rate it should be possible to interpolate your signals to a regular sequence.

t = linspace(data(1,1),data(1,end),2*numel(data(1,:)));
data2 = interp1(data(1,:),data','pchip')';

Then since you have time-varying time-shift between the signals you shouldn't Fourier-transform the entire data-set - that will not give you all information of interest. That's where the short-time-Fourier-transform comes to the rescue, that is the function spectrogram:

clf
Ts = mean(diff(t));
[S1,F1,T1] = spectrogram(data2(2,:),4*1024,1024,[],1/Ts);
[S2,F2,T2] = spectrogram(data2(3,:),4*1024,1024,[],1/Ts);
[S3,F3,T3] = spectrogram(data2(4,:),4*1024,1024,[],1/Ts);
subplot(3,2,1)
pcolor(T1,F1,log10(abs(S2))),shading flat,caxis([-2 3.5]),
ax = axis;             
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
colormap(jet)
try
  freezeColors
catch
    % Useful tool on FEX
end
subplot(3,2,3)
pcolor(T1,F1,log10(abs(S2))),shading flat,caxis([-2 3.5]),
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
try   
  freezeColors 
catch
  % Useful tool on FEX
end
subplot(3,2,5)         
pcolor(T3,F3,log10(abs(S3))),shading flat,caxis([-2 3.5]),
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
try   
  freezeColors 
catch
  % Useful tool on FEX
end

subplot(3,2,2)
pcolor(T3,F3,angle(S1.*conj(S2))),shading flat,caxis([-1 1]*pi),
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
colormap(hsv)
colorbar
subplot(3,2,4)         
pcolor(T3,F3,angle(S1.*conj(S3))),shading flat,caxis([-1 1]*pi),
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
colorbar
subplot(3,2,6)
pcolor(T3,F3,angle(S2.*conj(S3))),shading flat,caxis([-1 1]*pi),
axis([ax(1:2),2e4 5e6])
set(gca,'YScale','log')
colorbar

There in the left column you have the PSD of the 2nd 3rtd and 4th rows in data2 and in the right column you have the cross-phases of the 3 combinations. From there you can extract the frequencies of the amplitude-peaks and the corresponding frequency-shifts. As you see the frequencies vary with time, as does the cross-phase between the 1st and second as well as the 2nd and 3rd, from ~0 to ~pi (at around 0.4e-3 time-units).

This is how you find phase-shifts, but since the spectra of your signals varies with time, you should also have a look at the time-shifts between peaks and minimas, both of the signals and their slopes.