  Parametric down-conversion (PDC) forms one of the basic building blocks for
quantum optical experiments. However, the intrinsic multimode spectral-temporal
structure of pulsed PDC often poses a severe hindrance for the direct
implementation of the heralding of pure single-photon states or, for example,
continuous-variable entanglement distillation experiments. To get rid of
multimode effects narrowband frequency filtering is frequently applied to
achieve a single-mode behavior.
  A rigorous theoretical description to accurately describe the effects of
filtering on PDC, however, is still missing. To date, the theoretical models of
filtered PDC are rooted in the discrete-variable domain and only account for
filtering in the low gain regime, where only a few photon pairs are emitted at
any single point in time. In this paper we extend these theoretical
descriptions and put forward a simple model, which is able to accurately
describe the effects of filtering on PDC in the continuous-variable domain.
  This developed straightforward theoretical framework enables us to accurately
quantify the trade-off between suppression of higher-order modes, reduced
purity and lowered Einstein-Podolsky-Rosen (EPR) entanglement, when narrowband
filters are applied to multimode type-II PDC.
