  We investigate the spin excitation spectra in chiral and polar magnets by the
linear spin-wave theory for an effective spin model with symmetric and
antisymmetric long-range interactions. In one dimension, we obtain the analytic
form of the dynamical spin structure factor for proper-screw and cycloidal
helical spin states with uniform twists, which shows a gapless mode with strong
intensity at the helical wave number. When introducing spin anisotropy in the
symmetric interactions, we numerically show that the stable spin spirals become
elliptically anisotropic with nonuniform twists and the spin excitation is
gapped. In higher dimensions, we find that similar anisotropy stabilizes
multiple-$Q$ spin states, such as vortex crystals and hedgehog lattices. We
show that the anisotropy in these states manifests itself in the dynamical spin
structure factor: a strong intensity in the transverse components to the wave
number appears only when the helical wave vector and the corresponding easy
axis are perpendicular to each other. Our findings could be useful not only to
identify the spin structure but also to deduce the stabilization mechanism by
inelastic neutron scattering measurements.
