You have a function, that is defined on what seems to be roughly the interval [0,220]. Since you have not given us any data, only a picture of that data, I'll make something up to show an example.
y = exp(-((x-110)/50).^2)*12 - 6;
Now you wish to perform the periodic extrapolation of this function onto the real line.
xdomain = [min(x),max(x)];
extrapfun = @(X) fnval(smallspl,xdomain(1)+ mod(X-xdomain(1),diff(xdomain)));
fplot(extrapfun,[-1000,1000])
So the fully periodic extrapolation of this form onto the real line. I used fnval, which presumes the curve fitting toolbox, but you could have used ppval instead. And if makima does not work for you, you could have used pchip to create the spline. Or you could have used spline.
