Synchronising two different signals

Hello,

I am quite new to signal processing and I am trying my best to synchronize and align two signals that come from different devices.

One has a sample rate of 50 Hz and is recording acceleration with 3 axis (x, y and z). The other is recording ECG at 250Hz.

I have time marks of when both devices are turned on and off (which is different by max 10-20 seconds). Both seems to have 'time-drift', meaning that when looking at the data size, it never perfectly equals the size of Time*SampleRate. And even after resampling the 250Hz signal at 50Hz both data sizes have a small difference.

I have been trying different methods to align those signals but there is always a little delay between the two of them and I don't know what to do. I tried removing the time drift, synchronizing them with time-series, even the cross-correlation (even though I am not sure this can work since one of my signal has 3 axis)… Nothing seems to work.

So is there a way to know if there is major problem in one of the signals ?

Or is there another way of aligning/synchronizing those signals ?

I linked the two unfiltered signals.

Thanks,

Marine

[Star Strider]

What are we to do with these?

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1157478/Data.zip')

Uz = 1×8 cell array
    {'Data/'}    {'__MACOSX/._Data'}    {'Data/.DS_Store'}    {'__MACOSX/Data/._.DS_Store'}    {'Data/ECG.csv'}    {'__MACOSX/Data/._ECG.csv'}    {'Data/Acceleration.csv'}    {'__MACOSX/Data/._Acceleration.csv'}

EKG = readtable(Uz{5})

EKG = 904000×1 table
    ECG_DATA
    ________

       680  
      1372  
      1740  
      1774  
      1805  
      1832  
      1853  
      1870  
      1883  
      1889  
      1884  
      1870  
      1850  
      1832  
      1815  
      1800  

Acc = readtable(Uz{7})

Acc = 181412×18 table
    Var1    Var2    Var3     Var4    Var5    Var6    Var7    Var8    Var9            Var10             Var11    Var12    Var13    Var14     Var15    Var16    Var17    Var18
    ____    ____    _____    ____    ____    ____    ____    ____    ____    ______________________    _____    _____    _____    ______    _____    _____    _____    _____

    -106    -203    -1969    -157    151     -17      -32      54    -178    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      18     -87    -2052    -169    159     -17     -230     309    -296    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     129     -13    -2062    -169    151     -13     -140     245    -250    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     108     -85    -2073    -159    149     -23      -93     166    -129    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      66    -152    -2119    -169    149     -15       47      89    -143    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      81    -114    -2010    -165    145     -11      116       4    -155    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      59    -109    -2118    -170    148     -26       68      77    -144    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     154     -53    -1999    -163    143     -25      189     -35    -117    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     125      12    -1975    -158    156     -26      221    -132      56    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
       9    -110    -2064    -162    142     -20      220    -267     108    {'22-10-11T09:55:47Z'}     105      266      236     1016.5    0.06     25.17       0      4.1 
     -59    -226    -1893    -162    152     -26      220    -182      78    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
    -107    -329    -2100    -160    152     -22     -321     271    -124    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      13    -156    -2148    -158    154     -28     -371     359    -235    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     197      -5    -2076    -166    154     -26     -249     290    -205    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
     175     -65    -2140    -162    154     -22       21      32     -70    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 
      84    -178    -1973    -159    141     -27      201    -198     -47    {0×0 char            }     NaN      NaN      NaN        NaN     NaN       NaN     NaN      NaN 

Just looking at them, I have no idea.

.

[Marpe]

Yes sorry I forgot to share my code. This one of my trial to better understand.

Answer 1

[Star Strider]

I got this far, however I have no idea what you want to do with them at this point —

% clear
% close all
% datapathECG = %Data path;
% dECG = dir(datapathECG);
% nd = length(dir);

Uz = unzip('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1157478/Data.zip');
% EKG = readtable(Uz{5})
% Acc = readtable(Uz{7})


%ECG data
for n=10
%     file=[datapathECG,dECG(n).name];
%     tbl = readtable(file);
    tbl = readtable(Uz{5});
    ecg=table2array(tbl);
    [~,~]=size(ecg);
    Fs1 = 250;

    %Resampling of ECG from 250Hz to 50Hz
    ecg=resample(ecg,50,Fs1);
    [Necg,~]=size(ecg);
end

%Acceleration data
% close all  
% datapathAcc= % Data path to data files
% dAcc=dir(datapathAcc);
% nd=length(dir);

for n=5
%     file=[datapathAcc,dAcc(n).name];
%     tbl = readtable(file);
tbl = readtable(Uz{7});
    acctab=tbl(:,1:3);
    Tacc=tbl(:,10);
    acctab = table2array(acctab);
    [Nacc,dum]=size(acctab);
    Fs2=50;
end

%Remove drift in both
%ECG
StartECG = datetime(2022,10,11,07,56,40,'TimeZone','UTC');
StartECG.Format = 'hh:mm:ss';
Stop = datetime(2022,10,11,08,57,10,'TimeZone','UTC');
Stop.Format = 'hh:mm:ss';
Fs = 50;
Time = seconds(Stop - StartECG);
Nth = (Time.*Fs);
drift = Nth - Necg;
drift = drift/Fs;
drift = Nth/drift;
drift1 = round(drift/Fs);
ecg(drift1:drift1:end,:) = [];
[Necg,d]=size(ecg);


%Acceleration
DT = datetime(Tacc.Var10, 'InputFormat','yy-MM-dd''T''HHH:mm:ss''Z''','TimeZone','UTC');
DT.Format = 'hh:mm:ss';
DTnew = fillmissing(DT,'linear');
StartR = DTnew(1,1);
disp('Real  = ');

Real  = 

disp(StartR);

   09:55:47

StartR = datetime(StartR,"TimeZone","UTC");
StartR.Format = 'hh:mm:ss';

%Have to change everytime
StartTH = datetime(2022,10,11,07,55,20,'TimeZone','UTC');
StartTH.Format = 'hh:mm:ss';

disp('Theory  = ');

Theory  = 

disp(StartTH);

   07:55:20

delay = abs(StartR - StartTH);

StartACC = StartR - delay;
Stop = datetime(2022,10,11,08,56,10,'TimeZone','UTC');
Stop.Format = 'hh:mm:ss';
Fs = 50;
Time = seconds(Stop - StartACC);
Nth = (Time.*Fs);
drift = Nth - Nacc;
drift = drift/Fs;
drift = Nth/drift;
drift2 = round(drift/Fs);
acctab(drift2:drift2:end,:) = [];
[Nacc,d]=size(acctab);

%Time for ECG
time=StartECG;
time.Format= 'hh:mm:ss';
s1=seconds(1/Fs2:1/Fs2:Necg/Fs2);
T=time+s1;
Tecg = timetable(T',ecg);

%Time for Acceleration data
time=StartACC;
time.Format= 'hh:mm:ss';
s1=seconds(1/Fs2:1/Fs2:Nacc/Fs2);
T=time+s1;

Tacc = timetable(T',acctab);

TT = synchronize(Tecg,Tacc,"union","nearest");
stackedplot(TT.Time,TT.Variables);

Or, to put it differently, I do not see a problem. You have several different signals all sharing the same time vector. (I have no idea what they refer to, or what you want to wo with them.)

.

[Marpe]

Well, I want to align the ECG and Acceleration signals.

In the plot what you can see is ECG on top and then three axis (x, y ,z) of the acceleration data.

They seem aligned but when you zoom in you can see that even between first and second column some artifacts are not aligned. And that, I think, is not normal since those devices recorded the same movement as they were placed approximately at the same place.

What I did was like that:

First step for me would be to downsample the ECG data that has a 250Hz samplerate.

Afterwhat, normally if there wasn't any problem, the two data sets of ECG and acceleration should have the same size, right ? But there are not.

So that is why I am trying to remove the 'time-drift' of those two by using the exact UTC time at which I started and stopped both devices.

Even with all this and the synchronize function at the end, I can still see a small delay.

Maybe I am doing this wrong or maybe I am missing something.

[Star Strider]

The ECG signal (that I assume is ‘Column 1’) does not look like an ECG signal to me. The amplitudes are all wrong and there is significant noise.

Are you attempting to demonstrate postural effect (or something else) on heart rate? The ECG is going to have some sort of delay in response to any external disturbance simply because that is the way physiology works.

What effect do you intend to demonstrate?

[Marpe]

I am trying to demonstrate a correlation between ECG and BCG (ballistocardiogram acquired from the acceleration data).

Here the data is raw and unfiltered, that's why there is a lot of noise and that the ECG signal is not good.

If it's normal that there is delay then just how can I make sure or is there a way to know that I am synchronizing the two signals correctly ?

[Star Strider]

I have never done anything with ballistocardiography. An interesting study is Estimation of the respiratory rate from ballistocardiograms using the Hilbert transform and there are several other open-source articles in a Pub Med search i did just now, many of which appear to be interesting.

The data need to be pre-processed if you are to make any sense of them. First calculate Fourier transforms (fft or pspectrum) on all of them to determine the appropriate filter characteristics, then filter them. Geting rid of as much of the noise as possible is important.

There will be a delay between the ECG, pulse (most reliably detected and characterised by LED plethysmocardiography) and ballistocardiography signals because there is inherent inertia in all the physical responses. (There are delays between the carotid and pedal pulses simply because of the transit time of the pulse wave, the physical characteristics of the arterial system, and the distance between them, for example.) The ventricles require time after the ECG excitation signal to contract and then to eject the blood that filled them during diastole. They all have mass, viscosity, and elasticity. (I modeled all this decades ago simply out of curiosity and because I had easy access to all the signals. I am certain that much better models now exist that you could identify and estimate.) So when you have filtered the signals to get rid of as much of the noise as possible, it could be interesting to use the System Identification Toolbox functions to see if a model characterising them could be identified and estimated.

I leave that to you!

[Marpe]

Thank you very much for your help !

[Star Strider]

My pleasure!