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We propose a new filter, a smooth-$k$ space filter, to use in thePress-Schechter approach to model the dark matter halo mass function whichovercomes shortcomings of other filters. We test this against the mass functionmeasured in N-body simulations. We find that the commonly used sharp-$k$ filterfails to reproduce the behaviour of the halo mass function at low massesmeasured from simulations of models with a sharp truncation in the linear powerspectrum. We show that the predictions with our new filter agree with thesimulation results over a wider range of halo masses for both damped andundamped power spectra than is the case with the sharp-$k$ and real-spacetop-hat filters.

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