  Analysis of cosmic microwave background (CMB) datasets typically requires
some filtering of the raw time-ordered data. Filtering is frequently used to
minimize the impact of low frequency noise, atmospheric contributions and/or
scan synchronous signals on the resulting maps. In this work we explicitly
construct a general filtering operator, which can unambiguously remove any set
of unwanted modes in the data, and then amend the map-making procedure in order
to incorporate and correct for it. We show that such an approach is
mathematically equivalent to the solution of a problem in which the sky signal
and unwanted modes are estimated simultaneously and the latter are marginalized
over. We investigate the conditions under which this amended map-making
procedure can render an unbiased estimate of the sky signal in realistic
circumstances. We then study the effects of time-domain filtering on the noise
correlation structure in the map domain, as well as impact it may have on the
performance of the popular pseudo-spectrum estimators. We conclude that
although maps produced by the proposed estimators arguably provide the most
faithful representation of the sky possible given the data, they may not
straightforwardly lead to the best constraints on the power spectra of the
underlying sky signal and special care may need to be taken to ensure this is
the case. By contrast, simplified map-makers which do not explicitly correct
for time-domain filtering, but leave it to subsequent steps in the data
analysis, may perform equally well and be easier and faster to implement. We
focus on polarization-sensitive measurements targeting the B-mode component of
the CMB signal and apply the proposed methods to realistic simulations based on
characteristics of an actual CMB polarization experiment, POLARBEAR.
