Interpolation and missing values

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.')

[Image Analyst]

To determine "hole" or "gap" size, it helps to have the Image Processing Toolbox. Do you have that? Type ver to find out. If you do you can use functions like bwareaopen() or regionprops() to easily determine the size of the hole.

[Chad Greene]

Here is a loop that almost solves the problem. I'd rather avoid loops, but the biggest problem with this solution is the little tails that persist:

x = 0:.02:15; 
y = sin(x); 
x([3 25 32:33 200:280 410:415]) = []; 
y([3 25 32:33 200:280 410:415]) = []; 

plot(x,y,'ko'); hold on

xi = 0:.015:15;
yi = interp1(x,y,xi,'cubic'); 

for n = 1:length(xi)
    if min(abs(xi(n)-x))>.1
        yi(n) = NaN; 
    end
end

plot(xi,yi,'b.')

Above, a threshold is set to set to change any values more than 0.1 x units away from an x data point to NaN.

[Chad Greene]

I do have the Image Processing Toolbox, and I'm reading the documentation right now. Application of bwareaopen and regionprops is not immediately apparent.

Answer 1

[Paul]

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]

This works well; thank you!

[Image Analyst]

Well I couldn't get it to work but you did so that's all that counts:

clc;    % Clear the command window.
close all;  % Close all figures (except those of imtool.)
clear;  % Erase all existing variables. Or clearvars if you want.
workspace;  % Make sure the workspace panel is showing.
format long g;
format compact;
fontSize = 18;
% 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 data
subplot(3,1,1);
plot(x, y, 'ro-');
grid on;
title('Original Signal', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Units', 'Normalized', 'OuterPosition', [0 0 1 1]);

xi = 0:.015:15;

x_gap = x(2:end)-x(1:end-1);
subplot(3,1,2);
bar(x_gap);
title('x_gap', 'FontSize', fontSize, 'Interpreter', 'None');

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;
% Plot interpolated arrays.
subplot(3,1,3);
title('Interpolated Signal', 'FontSize', fontSize);
plot(xi, yi, 'bs-');

And I won't bother with using regionprops() since you already found a working solution.

[Paul]

add this:

yi = interp1(x,y,xi,'cubic');

after xi = 0:.015:15; and then it works.

[Chad Greene]

I turned Paul's solution into a function: http://www.mathworks.com/matlabcentral/fileexchange/45842. Thank you both for your help.