# Interpolation and missing values

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Chad Greene on 21 Feb 2014
Commented: Chad Greene on 11 Mar 2014
I have a series of data given by an x array and a corresponding y array. The arrays are equal in size. The x array is approximately equally spaced, but it has a few small gaps, and some very large gaps. I would like to interpolate to get numeric values in the small gaps, but I'd like to replace the big gaps with NaNs.
Here is an example of some small gaps, and one big gap. I'd like to replace the obviously incorrect interpolation with NaNs. How can I do this?
% create some data:
x = 0:.02:15;
y = sin(x);
% create some holes in the data
x([3 25 32:33 200:280 410:415]) = [];
y([3 25 32:33 200:280 410:415]) = [];
plot(x,y,'ko'); hold on
% the interpolation I'd like to improve:
xi = 0:.015:15;
yi = interp1(x,y,xi,'cubic');
plot(xi,yi,'b.')
Chad Greene on 21 Feb 2014
I do have the Image Processing Toolbox, and I'm reading the documentation right now. Application of bwareaopen and regionprops is not immediately apparent.

Paul on 21 Feb 2014
x_gap = x(2:end)-x(1:end-1);
ind=find(x_gap>0.025);
ind_int=[];
for j=1:numel(ind)
ind_int = [ind_int,find((xi>x(ind(j)) & xi<x(ind(j)+1)))];
end
yi(ind_int)=NaN;
Chad Greene on 11 Mar 2014
I turned Paul's solution into a function: http://www.mathworks.com/matlabcentral/fileexchange/45842. Thank you both for your help.