  We study the dynamics of a quantum walker simultaneously subjected to
time-independent and -dependent phases. Such dynamics emulates a charged
quantum particle in a lattice subjected to a superposition of static and
harmonic electric fields. With proper settings, we investigate the possibility
to induce Bloch-like super-oscillations, resulting from a close tuning of the
frequency of the harmonic phase $\omega$ and that associated with the regular
Bloch-like oscillations $\omega_B$ . By exploring the frequency spectra of the
wavepacket centroid, we are able to distinguish the regimes on which regular
and super-Bloch oscillations are predominant. Furthermore, we show that under
exact resonant conditions $\omega=\omega_B$ unidirectional motion is
established with the wavepacket average velocity being a function of the
quantum walk coin operator parameter, the relative strengths of the static and
harmonic terms, as well as the own phase of the harmonic phase. We show that
the average drift velocity can be well described within a continuous-time
analogous model.
