How to interpolate midpoints in a curve

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.

[Matt J]

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

[Proman]

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

Answer 1

[Matt J]

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.

[Image Analyst]

Quantum: Try adjusting the parameters to findpeaks() like MinPeakHeight or Threshold or something to get just a single peak in those regions.

[Proman]

Matt J.: Many thanks. Unfortunately, I failed to notice that findpeaks command appears to be disappointing for such problems. Thanks for your carefulness.

Image Analyst: Many thanks for your help and hint. It actually worked and improved the situations yet the code fails to work for both minima and maxima. I can not force the findpeaks with MinPeakHeight arguement to act the same for both minima and maxima. Any suggestions that how I can overcome this for both minima and maxiam according to my data?

[Matt J]

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

[Proman]

What a miracle this filter is *_*

Thanks again for your care and extremely productive help so far my friend!