  A variety of techniques have been developed for the approximation of
non-periodic functions. In particular, there are approximation techniques based
on rank-$1$ lattices and transformed rank-$1$ lattices, including methods that
use sampling sets consisting of Chebyshev- and tent-transformed nodes. We
compare these methods with a parameterized transformed Fourier system that
yields similar $\ell_2$-approximation errors.
