  In this paper we construct directionally sensitive functions that can be
viewed as directional time-frequency representations. We call such a sequence a
rotational uniform covering frame and by studying rotations of the frame, we
derive the rotational Fourier scattering transform and the truncated rotational
Fourier scattering transform. We prove that both operators are rotationally
invariant, are bounded above and below, are non-expansive, and contract small
translations and additive diffeomorphisms. We also construct finite uniform
covering frames.
