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

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Teshan Rezel
Teshan Rezel 2021년 5월 26일
댓글: Mathieu NOE 2021년 5월 27일
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

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Mathieu NOE
Mathieu NOE 2021년 5월 26일
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);

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