How to normalize curves with multiple peaks such that each peak will be 1 and each valley will be 0?

Hello,

I am looking for a way to normalize curves with multiple peaks such that each local maximum and minimum will be set to 1 and 0 respectively, and that the values between the maxima and minima will be set accordingly.

Thanks,

Haguy.

[dpb]

Only thing comes to mind would be to find each max/min pair and compute the necessary factor for those positions and then interpolate that scaling factor between each.

Providing an example data set would probably be beneficial.

[Haguy Wolfenson]

Thanks. That's what I was thinking. Is there a specific function for that?

This would be an example for a data set:

  7.758833 
  9.813105 
  11.43802 
  10.68728 
  6.67001 
  0.737689 
  -4.47406 
  -6.98998 
  -6.52002 
  -4.11176 
  -1.15441 
  1.4053 
  3.232571 
  4.339376 
  4.729456 
  4.145157 
  2.181519 
  -1.10699 
  -4.71235 
  -7.04357 
  -6.92214 
  -4.30292 
   -0.38969 
  2.694517 
  2.948959 
  0.215726 
  -2.97796 
  -2.9788 
  1.951206 
  9.78937 
  15.93909 
  16.79721 
  12.67508 
  7.168603 
  3.742826 
  3.560238 
  6.438025 
 12.06834 
 18.94483 
 23.36877 
 21.61921 
 13.23558 
 1.492308 
 -8.82432 
 -13.8726 
 -12.363 

Answer 1

[dpb]

If you mean 'builtin' already coded to do that, "No, I don't think so!" I've never seen it actually done before; don't think it's terribly common.

I don't have time to write full-blown code, but you should be able to follow along and write a function from a demo of the idea done at command line for the sample data--

y=x+abs(min(x));                             % move whole trace to baseline first
findpeaks(y)                                 % just to make the fancy plot
[pks,ipk]=findpeaks(y);                      % get the peaks, locations
[vlys,ivly]=findpeaks(-y);                   % and the valleys
vlys=-vlys;                                  % back to correct sign of signal
hold on
plot(ivly,vlys-1,'^r','MarkerFaceColor','r');% add markers for the valleys just for fun
b=polyfit([ipk(1) ivly(1)],[1/pks(1) 0],1);  % linear transformation peak-->1, valley-->0 first section
yhat=polyval(b,ipk(1):ivly(1));              % get the scale factor for the section
yhat=yhat.*y(ipk(1):ivly(1)).';              % and scale the actual data 
yyaxis right                                 % to plot the scaled on appropriate scale
hLy=plot((ipk(1):ivly(1)).',yhat,'k-');      % and plot that first section...
ylim([-0.2 1.6])                             % just to make origins aline left/right axes...
polyfit([ivly(1) ipk(2)],[0 1/pks(2)],1)     % now do the next section vly(1)-->0; pk(2)==>1
yhat=polyval(b,[ivly(1):ipk(2)]);            % and rinse and repeat above pattern...
yhat=yhat.*y(ivly(1):ipk(2)).';
hold on
hLy(2)=plot((ivly(1):ipk(2)).',yhat,'k-');
hLg=legend(hLy(1),'Normalized','Location','northwest');

Above yields inserted image; your mission, should you choose to accept it, is to take the above and turn it into the general function walking through the located peaks and valleys. You'll have to decide just what to do about the end sections where you don't have the alternate peak/valley to use to fully define the linear transformation...it's purely a guess as to what that scaling factor should

be as it is not known what the other extremum or its location would have been.

[Haguy Wolfenson]

Thanks a lot!

[xiaoxiaoliu xiaoxiaoliu]

what is 'hLy(1)' ?

What does it do here?

[dpb]

A missing line handle from plot ... code was pasted into Answers from command line and tried to clean up from the various pieces used to build the figure...missed adding the handles to the plot calls.

It is just one handle of the two in the array to only put one legend on the plot when there are multiple lines.

[xiaoxiaoliu xiaoxiaoliu]

Hello，dpb

How do you make the black normalization more natural, and how to normalize the black curve to the same length as the original data, （ handle the tail or add the tail）？

[xiaoxiaoliu xiaoxiaoliu]

This is the image from which your code runs，Thank you very much for your code.

[xiaoxiaoliu xiaoxiaoliu]

I found a formula for this solution, but I don't know how to program it.

%y is original data，max（i）is Local maximum; min(i) is Local minimum.

But I do not know how to write this program, I hope you can help me, thank you very much.

Answer 2

[Sargondjani]

Yeah, you would have to calculate a scaling factor for each peak/trough. In one dimension you can then use the scaling factor for each interval. In multiple dimensions you would have to interpolate the scaling factor.

[dpb]

That would be discontinuous tho, between the sections excepting in very unusual circumstances.

Answer 3

[xiaoxiaoliu xiaoxiaoliu]

How to normalize curves with multiple peaks such that each peak will be 1 and each valley will be -1？