MATLAB: De-noising blocky signal

blocky signalde-noisinghaarrectpulsewavelet

Hello everyone,
I have a signal and would like to transform it into a blocky signal. I looked into the wavelet toolbox and into the rectpulse function but I couldn't find a proper solution yet.
In the screenshot you can see my original signal and the desired result indicated in red. My signal is attached as well. Is there an easy way to achieve this?
I'm looking forward to your ideas.

Best Answer

I'd just just do something trivially simple here.
First, apply movstd. You want sequences where the curve is essentially constant. So a moving standard deviation on blocks of length 20 is a good start.
movlen = 20;
smov = movstd(g,[0,movlen-1]);
prctile(smov,50)
ans =
     0.051006
plot(smov,'.')
refline(0,.05)
So it looks like I can find essentially constant blocks. I'll just take the first block that movstd found with a standard deviation
figure
plot(g,'.b')
hold on
movlen = 20;
smov = movstd(g,[0,movlen - 1]); % forward window, of length movlen
tol = prctile(smov,50);
blocks = zeros(0,3);
bend = 0;
ng = numel(g);
nb = 0;
while true
  bstart = bend + find(smov(bend+1:(end - (movlen - 1))) <= tol,1,'first');
  if isempty(bstart)
    break
  end
  bend = bstart + movlen - 1;
  glevel = mean(g(bstart:bend));
    % accept the next point in the series as part of this
    % constant block if it is within tol*2 from glevel
    while ((bend + 1) <= ng) && (abs(g(bend+1) - glevel) < (2*tol)) 
      bend = bend + 1;
      glevel = mean(g(bstart:bend));
    end
    nb = nb + 1;
    blocks(nb,:) = [bstart bend, glevel];
    % add to the plot
    plot([bstart,bend],[glevel,glevel],'r-','linewidth',5)
  end
  grid on
These blocks were identified, where the series was essentially constant.
blocks
blocks =
         83          142        3.796
        189          224      0.74361
        226          245       1.0945
        266          299      0.74265
        301          335      0.28457
        355          377       4.1491
        394          460       4.1478
        479          499       4.0829
        566          594       4.1121
        595          706       4.0629
        743          766      0.59833
        767          826       0.6795
        835          857      0.71696
        886          965       4.1666
        966         1080       4.0353
       1084         1188        4.022
       1196         1226       1.5977
       1260         1291       4.0637
       1301         1374       1.5273
       1375         1405       1.6977
       1420         1440       1.7762
       1443         1464      0.45545
       1479         1505       1.5411
       1509         1536        1.055
       1537         1629      0.80301
       1639         1692       3.9861
       1693         1789       3.9074
       1821         1840       4.0813
Feel free to pick your own choice for the tolerance and window lengths. As you drew that plot to show your goal, my guess is you would want longer windows, with a somewhat larger tolerance.
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