# Interpolation of circular data

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Nicolas Bourbaki on 1 Sep 2021
Hello everybody out there using MATLAB,
Is there a built-in function for interpolating circular data, i.e. a timeseries of angles (in degree) between 0° and 360° to other timepoints.
I've carefully read the documentation for the interp1 function, which doesn't really mention this case, although this post is mentioning it.
This post is mentioning the interpft function, but I'm not sure whether this would help in my case.

Bjorn Gustavsson on 1 Sep 2021
To my understanding simply extend the input arrays such that you have a couple of points from the first few samples added onto the end adding 2*pi to those angles and a few points from the end of your arrays at the beginning subtracting 2*pi from those:
theta = linspace(0,2*pi-0.001,31);
f = 12*cos(theta) + 5*sin(3*theta).^2;
Theta = [theta(end-3:end)-2*pi,theta,theta(1:3)+2*pi];
F1 = [f(end-3:end),f,f(1:3)];
THETA = linspace(0,2*pi,301);
F2 = 12*cos(THETA) + 5*sin(3*THETA).^2;
Fi = interp1(Theta,F1,THETA,'pchip');
That way you force the interpolation to be periodic, you only need to braket your theta and f array with three (possibly 2 but I'm too lazy to check) points to get the cubic and spline interpolation-methods to give you a periodic interpolation.
HTH
Nicolas Bourbaki on 4 Sep 2021
Thanks, using `unwrap` was what is needed in this case.

R2021a

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