  We discuss the implementation details and the numerical performance of the
recently introduced nonconforming Trefftz virtual element method for the 2D
Helmholtz problem. In particular, we present a strategy to significantly reduce
the ill-conditioning of the original method; such a recipe is based on an
automatic filtering of the basis functions edge by edge, and therefore allows
for a notable reduction of the number of degrees of freedom. A widespread set
of numerical experiments, including an application to acoustic scattering, the
$h$-, $p$-, and $hp$-versions of the method, is presented. Moreover, a
comparison with other Trefftz-based methods for the Helmholtz problem shows
that this novel approach results in robust and effective performance.
