  The problem of suppressing the scattering from conductive objects is
addressed in terms of harmonic contrast reduction. A unique compact closed-form
solution for a surface impedance $Z_s(m,kr)$ is found in a straightforward
manner and without any approximation as a function of the harmonic index $m$
(scattering mode to suppress) and of the frequency regime $kr$ (product of
wavenumber $k$ and radius $r$ of the cloaked system) at any frequency regime.
In the quasi-static limit, mantle cloaking is obtained as a particular case for
$kr \ll 1$ and $m=0$. In addition, beyond quasi-static regime, impedance
coatings for a selected dominant harmonic wave can be designed with proper
dispersive behaviour, resulting in improved reduction levels and harmonic
filtering capability.
