  We perform the scattering analysis of the evolution operator of quantum walks
with an anisotropic coin, and we prove a weak limit theorem for their
asymptotic velocity. The quantum walks that we consider include one-defect
models, two-phase quantum walks, and topological phase quantum walks as special
cases. Our analysis is based on an abstract framework for the scattering theory
of unitary operators in a two-Hilbert spaces setting, which is of independent
interest.
