A new smooth-$k$ space filter approach to calculate halo abundances

We propose a new filter, a smooth-$k$ space filter, to use in the Press-Schechter approach to model the dark matter halo mass function which overcomes shortcomings of other filters. We test this against the mass function measured in N-body simulations. We find that the commonly used sharp-$k$ filter fails to reproduce the behaviour of the halo mass function at low masses measured from simulations of models with a sharp truncation in the linear power spectrum. We show that the predictions with our new filter agree with the simulation results over a wider range of halo masses for both damped and undamped power spectra than is the case with the sharp-$k$ and real-space top-hat filters.