Mean of an oscillatory trajectory

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Ban 2023-8-7

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https://ww2.mathworks.cn/matlabcentral/answers/2005862-mean-of-an-oscillatory-trajectory

回答： Image Analyst 2023-8-8

采纳的回答： Daniel Bengtson

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Hi,

I have a particle moving in oscillatory path. See the plot of distantce vs time plot. How do I find the mean trajectory ?

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Daniel Bengtson 2023-8-7

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https://ww2.mathworks.cn/matlabcentral/answers/2005862-mean-of-an-oscillatory-trajectory#answer_1284522

在 MATLAB Online 中打开

p = polyfit(t,X,2); % fit a second order polynomial to the data
newT = linspace(min(t),max(t)); % 100 evenly spaced steps over the range of t
Y = polyval(p,newT); % evaluate the polynomial at these steps
plot(newT,Y);

Nope, I didn't think too deep. Your strategy is a good one for this case. I was wondering about the mathematical definition of the mean trajectory, as well as if some data smoothing algorithms may work.

Daniel Bengtson 2023-8-8

I should have thought on it more before posting. You are right to question my answer. Polyfit is just a least squares regression and given that I did not take any steps to enforce an intercept at zero, and that the error between the theoretical mean trajectory and raw signal would be relatively small near zero compared to near t max, it probably isn't as good of a fit as it could have been.

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