Truncated basis ApproxFun


I would like to use ApproxFun.jl for a truncated FFT. Is it possible to create direct and inverse Fourier transforms spanned by a sparse basis?

This is what I have in mind:

using ApproxFun

S = Fourier()

n = 256
sparse_idx =  [1; 20; 30; 40]
T = ApproxFun.plan_transform(S, n)
Ti = ApproxFun.plan_itransform(S, n)

T_sparse = ApproxFun.plan_transform(S, n, sparse_idx)
Ti_sparse = ApproxFun.plan_itransform(S, n, sparse_idx)