Interpolation - Fourier interpolant (i.e. trigonomentric) & Using Gauss-Legendre polynomial

For example, f(x) = cos(x) in [-pi,pi]

1)I want to find Fourier(trigonomentric) interpolant. Is there any built in function for this interpolation? (such as 'interp1') If not, how can I do? Please give me some useful link or hint!

2)I want to find Gauss-Legendre polynomial of degree n(specified) My note says that if I use Gauss points and weights on the interval [1,1] I can find it. But actually i even don't know about Gauss points. (So I tried in wiki, but there wasn't) Same as 1) someone can give me some useful link or hint? Surely, built in function is nice if it exists.

[John D'Errico]

No, interp1 does not offer a Fourier interpolant.

You have it backwards on the Gauss-Legendre. You get nodes and weights from the polynomials.

There is a legendre function in MATLAB, that does return Legendre polynomials. Or I recall that my sympoly toolbox does have an orthpoly tool in it, that allows generation of polynomial families of all the standard types, in sympoly form.

[Chaitral Date]

There is a function in MATLAB called as "interpft" which you can use for Fourier Interpolation. See the below link for more information,

http://www.mathworks.com/help/matlab/ref/interpft.html

If the above function does not serve the purpose, please let us know your used case.