How to curve fitting a cosine function with exponential decay tau?

Question

Mengyan Zhu 2020-10-6

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https://ww2.mathworks.cn/matlabcentral/answers/605636-how-to-curve-fitting-a-cosine-function-with-exponential-decay-tau

评论： Star Strider 2020-10-6

Hello,

I am new to MATLAB and I dont know how to fit a consine function. I have my data points and this is the function that I need to fit. I want to know the values of T, phi, and tau. How can I do that? If anyone could provide some insights, that would be greatly appreiciated!

This is my data for time and amplitude

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Alex Sha 2020-10-6

Hi, are you sure two pairs of data "4.6500 -1.0472" and "7.0333 -0.0789" are correct?

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Answer 1

Star Strider 2020-10-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/605636-how-to-curve-fitting-a-cosine-function-with-exponential-decay-tau#answer_505761

在 MATLAB Online 中打开

Try this:

y = detrend(y);                                                                 % Remove Linear Trend
yu = max(y);
yl = min(y);
yr = (yu-yl);                                                                   % Range of ‘y’
yz = y-yu+(yr/2);
zci = @(v) find(v(:).*circshift(v(:), [-1 0]) <= 0);                            % Returns Approximate Zero-Crossing Indices Of Argument Vector
zt = x(zci(y));
per = 2*mean(diff(zt));                                                         % Estimate period
ym = mean(y);                                                                   % Estimate offset
fit = @(b,x)  b(1) .* exp(x./b(2)) .* (cos(2*pi*x./b(3) + b(4))) + b(5);        % Objective Function to fit
fcn = @(b) norm(fit(b,x) - y);                                                  % Least-Squares cost function
[s,nmrs] = fminsearch(fcn, [yr; -10;  per;  -1;  ym])                           % Minimise Least-Squares
xp = linspace(min(x),max(x), 500);
figure
plot(x,y,'b', 'LineWidth',1.5)
hold on
plot(xp,fit(s,xp), '--r')
hold off
grid
ylim(ylim*1.5)
xlabel('Time')
ylabel('Amplitude')
legend('Original Data',  'Fitted Curve')
text(0.2*max(xlim),0.7*min(ylim), sprintf('$y = %.3f\\cdot e^{\\frac{t}{%.3f}}\\cdot cos(2\\pi \\frac{t}{%.3f} %+.3f)$', [s(1:2); 1./s(3:4)]), 'Interpreter','latex', 'FontSize',14)

producing:

It is essentially the code in my previous Answer that you already discovered,simply changed to fit your equation.

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Mengyan Zhu 2020-10-6

Thank you very much! Do you know how can I add x and y error bars for the points?

Star Strider 2020-10-6

My pleasure!

If you have error bars associated with them, use the errorbar function to plot the error bars. Recent releases can plot both x and y error bars, earlier releases can only plot y error bars. (I do not remember the release the x error bars were introduced.)

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