# how to maintain continuity and periodicity of a function

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Rose on 24 Jun 2013

I have a parameter (piece wise constant over each season of the year). I used 'pchip' to interpolate this function:

``` function y  =  mu(t)
xl = [0 23.3125 46.625 69.9375 114.5625 137.875 161.1875 205.8125 229.125 252.8125 297.0625 320.375 343.6875 365 ];
yl = [500 500 500 500 1500 1500 1500 500 500 500 0 0 0 0 ];
y = pchip(xl,yl,t);
end```

I used mod to make it periodic with a period of 365 days:

```M = mu(mod(tspan,365));
```

But i get a discontinuous and non-periodic function while going from t=364 to t=365. How can i make this function continuous and periodic? I didn't know how to attach a jpg file to my question, otherwise i would have attached a picture showing the function \$mu\$. Any kind of help will be appreciated.

Iain on 25 Jun 2013
Try ensuring that your fit wraps around - ie, that you give it x = 366 and y = the value it has when x = 0.
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Iain on 25 Jun 2013
I am saying that if you expand your curve to "look like" it continues on both ends, then your fit will be much more likely to be periodic.