Damped cosine features in a exponential decay

Hi Guys,

I am trying to fit a decay curve which has some oscillatory feature in the decay. I tried to fit the data with the sum of a exponential with cosine function but didn't succed. Any help would be appreciated. I attached file here (column 1 is time and column 2 is the corresponding intensities).

Thanks and regards,

[Mathieu NOE]

hello

I plotted your data

seems the data and the structure of the fit model will not match...

even by mentally removing the exponential trend, the remaining oscillations have variable amplitude and period as time goes... it will be tricky to find a combination of sinusoidal function that fits this portion of the signal

maybe a solution :

1. remove the exp trend
2. on the ramining signal, use zero crossing detection to compute cycle to cycle period (and therefore the instantaneaous frequency of a sinus signal)
3. to fit that, compute a sine signal with the period / amplitude observed in step 2

[Kunjanni]

Thanks a lot for your comments and for valuable suggestions.

Answer 1

[Star Strider]

This produces a reasonable approximation, however the signal appears to be changing its frequency toward the end:

D = load('Ampf.mat');
t = D.Ampf(:,1);
s = D.Ampf(:,2);

s = detrend(s,7);

yu = max(s);
yl = min(s);
yr = (yu-yl);                                                                   % Range of ‘y’
yz = s-yu+(yr/2);
zt = t(yz(:) .* circshift(yz(:),[1 0]) <= 0);                                   % Find zero-crossings
per = 2*mean(diff(zt));                                                         % Estimate period
ym = mean(s);                                                                   % Estimate offset
fit = @(b,x)  b(1) .* exp(b(2).*x) .* (sin(2*pi*x./b(3) + 2*pi/b(4))) + b(5);   % Objective Function to fit
fcn = @(b) norm(fit(b,t) - s);                                                  % Least-Squares cost function
B = fminsearch(fcn, [yr; -1;  per;  -1;  ym])                                   % Minimise Least-Squares
xp = linspace(min(t),max(t));
yp = fit(B,xp);

figure
plot(t, s, '-p')
hold on
plot(xp, yp, '-r')
hold off
grid

It may be necessary to change ‘fit’ to something more closely approximating the process that produced your data. Retain the detrending step in the code.

[Kunjanni]

Thanks a lot for your help :). It works for me.

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

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