How to interpolate midpoints in a curve

Question

Proman 2020-9-8

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/590755-how-to-interpolate-midpoints-in-a-curve

评论： Proman 2020-9-9

采纳的回答： Matt J

Data1.mat

在 MATLAB Online 中打开

Hello to everyone and greetings

I have a curve that I intend to find its midpoints (points between each succesive minimum and maximum) and connect them to each other to plot an envelope-wise curve like the following (the green dotted-dashed curve is the envelope I try to realize):

the code I used to plot this is the trivial approach (to my opinion):

clc
clear
close all
load Data1
figure
plot(t,R66)
xlabel('time (ps)')
ylabel('\rho_{66}')
[pks,max_loc] = findpeaks(R66,t);
invert_R66 = max(R66(:)) - R66;
[pksm,min_loc] = findpeaks(invert_R66,t);
pksm = max(R66(:)) - pksm;
xmid = (max_loc(2 : end) + min_loc) ./ 2;
xmid_p = (min(R66) + max_loc(1))  / 2;
ymid = interp1(t,R66,xmid);
ymid_p = interp1(t,R66,xmid_p);
xmid = [xmid_p xmid'];
ymid = [ymid_p ymid'];
hold on
plot(xmid,ymid,'r')
axis([0 700 0 0.045])
legend('Population','Restoration')

It quite worked well for every curve I gave as an input but the following curve (which its data is attached as Data1.mat) is not responding well as you can see

I somehow believe that there must be a problem with interpolation but after all, I can not figure out where I am going wrong. It would be kind of you to help me at this.

Thanks in advance for your time given on my question.

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Matt J 2020-9-8

编辑：Matt J 2020-9-8

The Data1.mat file contains several data sets. Which is the one that doesn't work?

Proman 2020-9-9

R66 is the one that goes wrong. Already indicated in the code

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Answer 1

Matt J 2020-9-9

1
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/590755-how-to-interpolate-midpoints-in-a-curve#answer_491842

编辑：Matt J 2020-9-9

The code is working fine. You think there is only one peak in the interval 200<=t<=300, but if you zoom in, you will see that there are three of them squished very close together. The same for the other intervals.

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Matt J 2020-9-9

编辑：Matt J 2020-9-9

在 MATLAB Online 中打开

A Savitzky-Golay pre-filter seems to help a lot.

load('Data1.mat')
close all
figure
procfun(R66,t)
function procfun(R,t)
 w=101; %window width
 Rsg = sgolayfilt(R,2,w);
 Rsg(1:w)=R(1:w);
 
 D=diff(sign(diff([Rsg(1);Rsg])))~=0;
 
 tp=t(D);
 tq=(tp(1:end-1)+tp(2:end))/2;
 
 Rq=interp1(t,R,tq);
 Rp=interp1(t,R,tp);
 pp=interp1(tq,Rq,'linear','pp');
 
 hold on 
  plot(t,R,tp,Rp,'rx');
  fplot(@(t)ppval(pp,t),[tq(1),t(end)])
  xlabel('time (ps)')
  ylabel('\rho_{66}')
 hold off
end