  We study the localization properties, energy spectra and coin-position
entanglement of the aperiodic discrete-time quantum walks. The aperiodicity is
described by spatially dependent quantum coins distributed on the lattice,
whose distribution is neither periodic (Bloch-like) nor random (Anderson-like).
Within transport properties we identified delocalized/localized quantum walks
mediated by a proper adjusting of aperiodic parameter. Both scenarios are
studied by exploring typical quantities (inverse participation ratio and
survival probability), as well as the energy spectra of an associated effective
Hamiltonian. By using the energy spectra analysis, we show that the early stage
the inhomogeneity leads to vanishing gap between two main bands, which
justifies the the delocalized character observed for $\nu<0.5$. With increase
of $\nu$ arises gaps and flat-bands on the energy spectra, which corroborates
the suppresion of transport detected for $\nu>0.5$. For $\nu$ high enough we
observe an energy spectra which resembles that described by the 1d Anderson
model. Within coin-position entanglement, we show many settings in which an
enhancement in the ability to entangle is observed. This behavior brings new
informations about the role played by aperiodicity on the coin-poisition
entanglement for static inhomogeneous systems, reported before as almost always
reducing the entanglement when comparing with the homogeneous case. We extend
the analysis in order to show that systems with static inhomogeneity are able
to exhibit asymptotic limit of entanglement.
