---
abstract: 'We describe a method performing $w$-projection using the fast Gauss transform of @Strain91. We derive the theoretical performance, and simulate the actual performance for a range of $w$ for a canonical array. While our implementation is dominated by overheads, we argue that this approach could for the basis of a higher-performing algorithms with particular application to the Square Kilometre Array.'
author:
- |
    K. W. Bannister$^{1,2,3}$[^1], T. J. Cornwell$^1$\
    $^{1}$CSIRO Astronomy and Space Science, PO Box 76, Epping NSW 1710, Australia\
    $^{2}$Bolton Fellow\
bibliography:
- 'Master.bib'
date: 'Accepted 2011 XXX XXX. Received XXX December XX; in original form XXX XXX XXX'
title: 'Memory-efficient $w$-projection with the fast Gauss transform'
---

\[firstpage\]

techniques: interferometric

Introduction
============

Interferometers are composed of an array of antennas arranged in a 3 dimensional volume. For long observations, even instantaneously planar arrays have baselines that are non-coplanar due to Earth rotation synthesis. Correcting non-coplanar baselines in interferometers require the use of a de-projection technique to compensate for the non-coplanarity. To date, $w$-projection [@Cornwell08] is the most computationally efficient algorithm known.

Interferometric images are usually formed by convolutional resampling of the measured visibilities on a regularly sampled, two dimensional $uv$ plane. Convolutional resampling operates by 