  Modern CMB analysis pipelines regularly employ complex time-domain filters,
beam models, masking, and other techniques during the production of sky maps
and their corresponding angular power spectra. However, these processes can
generate couplings between multipoles from the same spectrum and from different
spectra, in addition to the typical power attenuation. Within the context of
pseudo-$C_\ell$ based, MASTER-style analyses, the net effect of the time-domain
filtering is commonly approximated by a multiplicative transfer function,
$F_{\ell}$, that can fail to capture mode mixing and is dependent on the
spectrum of the signal. To address these shortcomings, we have developed a
simulation-based spectral correction approach that constructs a two-dimensional
transfer matrix, $J_{\ell\ell'}$, which contains information about mode mixing
in addition to mode attenuation. We demonstrate the application of this
approach on data from the first flight of the SPIDER balloon-borne CMB
experiment.
