Is there a way to smoothen the function/"bridge the gap"?

Hi folks,

I have a graph as follows. I am looking to replace the valley (red) with smoothened data. Is there a way to do this? I am unaware of the best method of achieving this currently.

Thanks

Answer 1

[Mathieu NOE]

hello

this would be me suggestion if the idea is to replace the "faulty" data segment with a piecewise linear segment and then do a further smoothing

    %--- Example #2: smooth a curve / wide valley removal ---
  x = linspace(0,100,256);
  y = cos(x/10)+(x/50).^2;
  y([70:120]) = - 2;
  y = y+ randn(size(x))/10;
  yy = y;
  
  % define segment to be removed based on sharp slope changes
  dy = gradient(y);
  % remove bad data "in the valley" 
  [val_min,ind_min] = min(dy);
  [val_max,ind_max] = max(dy);
  ind_offset = 2; % expand a bit the data segment beyond the limits ind_min / ind_max => ind_min-ind_offset / ind_max+ind_offset
  y(ind_min-ind_offset:ind_max+ind_offset) = linspace(y(ind_min-ind_offset),y(ind_max+ind_offset),ind_max-ind_min+1+2*ind_offset); % replace outliers by linear segment
    
  N = 25;
  ys = smoothdata(y,'gaussian',N); 
  figure (3);
  plot(x,yy,'b',x,y,'k',x,ys,'r-.','LineWidth',2);
  legend('raw data','interpolated data','interpolated and smoothed data')
  

now there is another possibility is to "shift" upwards this segement (if we want to keep the data) and do a smoothing as well

     %--- Example #3: shift the "valley" to be (more or less) aligned with rest of data ---
  x = linspace(0,100,256);
  y = cos(x/10)+(x/50).^2;
  y([70:120]) = - 2;
  y = y+ randn(size(x))/10;
  yy = y;
  
  % define segment to be shifted based on sharp slope changes
  dy = gradient(y);
  % remove bad data "in the valley" 
  [val_min,ind_min] = min(dy);
  [val_max,ind_max] = max(dy);
  ind_offset1 = 0; % expand a bit the data segment beyond the limits ind_min / ind_max => ind_min-ind_offset / ind_max+ind_offset
  ind_offset2 = 0; % expand a bit the data segment beyond the limits ind_min / ind_max => ind_min-ind_offset / ind_max+ind_offset
  delta = (y(ind_min-ind_offset1) + y(ind_max+ind_offset2))/2 -  mean(y(ind_min-ind_offset1:ind_max+ind_offset2));
  
  y(ind_min-ind_offset1:ind_max+ind_offset2) = y(ind_min-ind_offset1:ind_max+ind_offset2) + delta; % shift segment based on mean value
    
  N = 25;
  ys = smoothdata(y,'gaussian',N); 
  

[Teshan Rezel]

@Mathieu NOE this is perfect, thank you!

[Mathieu NOE]

My pleasure !