Is it possible to align two data sets with irregular sampling while preserving the respective indices?

I have 2 data sets. These measurements were taken on a test from different instruments at different sampling rates. There is a similarity in a way that when Data A becomes constant, Data B reaches the peak. There are various answers on the community but they have same sampling frequency. In this case the sampling is different and the sampling is not constant either. I want to align them without manually assigning anything. I also want to preserve the indexing of the original data points after alignment.

Currently, my code uses manual picking of points.

clc
clear all
close all
%% Load normalized data

ta = load('ta.mat'); ta = ta.ta;
tu = load('tu.mat'); tu = tu.tu;
xa = load('xa.mat'); xa = xa.xa;
xu = load('xu.mat'); xu = xu.xu;

%% Plotting the data
figure
tiledlayout(1,2)
nexttile
plot (ta,xa)
hold on
plot (tu,xu)
legend('Data A','Data UT', Location='southeast')


tanew = ta + 360.655; % I have identified the difference manually

nexttile
plot (tanew,xa)
hold on
plot (tu,xu)
legend('Data Anew','Data UT', Location='southeast')

I would appreciate your help in this regard.

Good day

Answer 1

[Mathieu NOE]

hello

I gave it a try and this is my best result so far

first I simply used the time delat between the red dots (easy solution but not the best result) , then I refined the code and used the green dots

result

code

clc
clear all
close all
%% Load normalized data
load('ta.mat'); 
load('tu.mat'); 
load('xa.mat'); 
load('xu.mat'); 

% ta / xa : get start and finish points of first flat sections (for ta < 1000)
ta_diff = [0 ; diff(ta(ta<1000))];
[val,idx] = max(ta_diff);
ta_flat1_start = ta(idx-1);
xa_flat1_start = xa(idx-1);
ta_flat1_end = ta(idx);
xa_flat1_end = xa(idx);

% tu / xu : get first peak above y threshold = xa_flat1_end
minpeakdist = 200; % minpeakdist is the minimum desired distance between peaks (optional, defaults to 1)
 [LOCS1, PKS1]=peakseek(xu,minpeakdist,xa_flat1_end); % you can probably get similar results with findpeaks for those who prefer
 % find valleys (end of exp decay) by using the negated (and smoothed) xu data
 xus = smoothdata(xu,'sgolay',30,'degree',1);
[LOCS2, PKS2]=peakseek(-xus,minpeakdist);
LOCS2 = LOCS2(LOCS2>LOCS1(1)); % get LOCS2 indices for LOCS2 above LOCS1(1)
tu2 = tu(LOCS2(1)); % get tu values accordingly
xu2 = xu(tu>tu2); % get xu values accordingly
idx_tu2_refined = find(xu2>xu(LOCS2(1))+1e-3,1,'first'); % we are looking for a few samples latter than the knee itself
 % time delta = td
 td = tu(LOCS2(1)+idx_tu2_refined) - ta_flat1_end;


%% Plotting the data
figure
tiledlayout(1,2)
nexttile
plot (ta,xa,'+-',ta_flat1_start,xa_flat1_start,'dr',ta_flat1_end,xa_flat1_end,'dg',...
    tu,xu,'+-',tu,xus,'-',tu(LOCS1(1)),xu(LOCS1(1)),'*r',tu(LOCS2(1)+idx_tu2_refined),xu(LOCS2(1)+idx_tu2_refined),'*g');
% legend('Data A','Data UT', 'Location','southeast')
% tanew = ta + 360.655; % I have identified the difference manually
tanew = ta + td; % I have identified the difference automatically
nexttile
plot (tanew,xa,tu,xu)
% legend('Data Anew','Data UT', 'Location','southeast')

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [locs, pks]=peakseek(x,minpeakdist,minpeakh)
% x is a vector input (generally a timecourse)
% minpeakdist is the minimum desired distance between peaks (optional, defaults to 1)
% minpeakh is the minimum height of a peak (optional)
%
% (c) 2010
% Peter O'Connor
% peter<dot>ed<dot>oconnor .AT. gmail<dot>com
if size(x,2)==1, x=x'; end
% Find all maxima and ties
locs=find(x(2:end-1)>=x(1:end-2) & x(2:end-1)>=x(3:end))+1;
if nargin<2, minpeakdist=1; end % If no minpeakdist specified, default to 1.
if nargin>2 % If there's a minpeakheight
    locs(x(locs)<=minpeakh)=[];
end
if minpeakdist>1
    while 1
        del=diff(locs)<minpeakdist;
        if ~any(del), break; end
        pks=x(locs);
        [garb, mins]=min([pks(del) ; pks([false del])]); %#ok<ASGLU>
        deln=find(del);
        deln=[deln(mins==1) deln(mins==2)+1];
        locs(deln)=[];
    end
end
if nargout>1
    pks=x(locs);
end
end

[UH]

Mathieu NOE, thanks a bunch for your valuable time on extensive analysis of this code. This seems complicated for my brain to digest (I am still working on the code to understand and apply further on my data). However, if I make a few compromises (I ignore preservation of the indexing and just align the charts with respect to the x-axis only), can the procedure be simplified?

For example if the indexing is ignored and I just want to align the signals and simply resample them to match their timing (so that I can plot a relation between the respective xa and xu).

thanks.

[Mathieu NOE]

hello again

we can use interp1 to have a common x axis , but I am not sure what your really mean by "keeping" (or not) the indexing ? what index ?

is the result obtained so far matching your expectations or did I miss something ?

Answer 2

[Image Analyst]

Point set matching is a difficult problem. I suggest you start here:

https://en.wikipedia.org/wiki/Point-set_registration

https://www.google.com/search?q=point+set+matching+problem&source=hp&ei=x1JjY7fVHK6i5NoPh8-YmAo&iflsig=AJiK0e8AAAAAY2Ng19fc0EOyxNACQ1rxNJmrYjth9QGQ&oq=point+set+matchin&gs_lp=Egdnd3Mtd2l6uAEB-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&sclient=gws-wiz