# From top-hat masking to smooth transitions: P-filter and its application to polarized microwave sky maps

## TL;DR

This paper introduces P-filters, a semi-analytic function that extends top-hat masking in CMB analysis, reducing leakage problems while maintaining continuity and outperforming traditional masks.

## Contribution

The paper proposes P-filters that improve upon top-hat masking by reducing leakage and ensuring smooth transitions, with demonstrated advantages over existing masking techniques.

## Key findings

- P-filters significantly reduce leakage in CMB polarization maps.
- P-filters outperform traditional masks in WMAP and Planck data.
- P-filters have potential to replace standard masking methods.

## Abstract

In CMB science, the simplest idea to remove a contaminated sky region is to multiply the sky map with a mask that is 0 for the contaminated region and 1 elsewhere, which is also called a top-hat masking. Although it is easy to use, such top-hat masking is known to suffer from various leakage problems. Therefore, we want to extend the top-hat masking to a series of semi-analytic functions called the P-filters. Most importantly, the P-filters can seamlessly realize the core idea of masking in CMB science, and, meanwhile, guarantee continuity up to the first derivative everywhere. The P-filters can significantly reduce many leakage problems without additional cost, including the leakages due to low-, high-, and band-pass filtering, and the E-to-E, B-to-B, B-to-E, and E-to-B leakages. The workings of the P-filter are illustrated by using the WMAP and Planck polarization sky maps. By comparison to the corresponding WMAP/Planck masks, we show that the P-filter performs much better than top-hat masking, and meanwhile, has the potential to supersede the principal idea of masking in CMB science. Compared to mask apodization, the P-filter is ``outward'', that tends to make proper use of the region that was marked as 0; whereas apodization is ``inward'', that always kills more signal in the region marked as 1.