Plotting a peak envelope

I have measured the swinging off of a resonant circuit with a oscilloscope. Now I'm trying to fit a peak envelope over this data. Therefore I've tried:

figure 
plot(temp(:,1), smooth(temp(:,2),30)) 
hold on 
plot(temp(:,1), smooth(abs(hilbert(temp(:,2))),190))

I still get a slightly oscillating function, instead of a constantly decreasing function. How can I improve the envelope function? Would really appreciate help. My solution is shown in the image. Cheers

 P.s.: For the argument of smooth(x,y) I iteratively worked out optimal values

Answer 1

[Star Strider]

I don’t have your signal, so I can’t provide definitive code.

First, do a fft of your signal so you have an idea of the frequency content.

Second, experiment with the envelope function (or its equivalent, the hilbert call you’ve already used) but without the smooth call:

y = abs(hilbert(temp(:,2)));

You may have to adjust the parameters of the hilbert function.

Another possibility is to use a bandpass filter, and just experiment with the passbands until your get the result you want. Use the results of the fft call for your design. The objective is to pass only the low-frequency envelope of the function.

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EDIT —

This isn’t perfect, but it’s the best I can do:

[d,s,r] = xlsread('Camill Trüeb F0002CH1.csv', 'E1:E2500');
Ts = 4E-10;
Fs = 1/Ts;
Fn = Fs/2;
tv = (0:length(d)-1)*Ts;
st = find(d > 0.1, 1, 'first');
d = d(st:end);
tv = tv(st:end);
L = length(d);

[pks, locs] = findpeaks(abs(d), tv, 'MinPeakDist',1E-7);
q = [locs' ones(size(locs'))]\log(abs(pks));                    % Initial Parameter Estimaes
fitfcn = @(b,t) b(1) .* exp(b(2).*t) + b(3);                    % Fit Function
SSECF = @(b) sum((pks - fitfcn(b,locs')).^2);                   % Cost Function

[B,SSE] = fminsearch(SSECF, [pks(1); q(1); 0]);

figure(5)
plot(tv, d)
hold on
plot(tv, fitfcn(B,tv))
hold off
grid

[Camill Trüeb]

Dear Star Strider

Thank you a thousand times! Your fitfunction approach with the cost function works way better than mine. Over all the different data sets the results are being very good. I don't think there is a perfect solution, since my measurements do have a slight offset at the first 1-2 peaks, as a result of a loading of the resonator. Again thank you very much Camill

[Star Strider]

As always, my pleasure!

Answer 2

[Camill Trüeb]

Thank you both for the fast answers! I've now worked out the first method with findpeaks. I smooth my data, use findpeaks and fit an exponential curve on to the solutions. The solution is ok, but there is still space for improvement. @Star Strider: Unfortunately I don't have any experience with filter design and I didn't manage to change parameters of the hilbert function. When simply using abs(hilbert(data)) I don't get a good solution. I attached a set of data to this answer, maybe you could help me out with more concrete code. Thanks already!

Answer 3

[Greg Dionne]

If you have HILBERT then you have access to the Signal Processing Toolbox. If you have R2015b or later, try using ENVELOPE:

[d,s,r] = xlsread('F0002CH1.csv', 'E1:E2500')
%zoom in on decaying portion
envelope(d(580:end),500,'analytic')

[Camill Trüeb]

That's what I first wanted to use. But I have 2015a as well as 2016a and none of them knows ENVELOPE. Is there a possibility this function only exists in 2015b?

[Greg Dionne]

It should be in 16a.

 cd ([matlabroot '/toolbox/signal/signal'])
 edit envelope

Hopefully it'll be there.