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
