# Introduction

Our goal is efficient and robust numerical evaluation of Fourier integrals of the form $f(\vec{r}) = N_n(a,b) \int\, d^n k\, e^{+b i (\vec{k}\cdot\vec{r})}\, \tilde{f}(\vec{k}) \quad , \quad \tilde{f}(\vec{k}) = \tilde{N}_n(a,b) \int\, d^n r\, e^{-b i (\vec{k}\cdot\vec{r})}\,f(\vec{r}) \; , \label{eqn:fourier}$ with normalization factors $N_n(a,b) = |b|^{n/2} (2\pi)^{-n(1+a)/2} \quad , \quad \tilde{N}_n(a,b) = |b|^{n/2} (2\pi)^{-n(1-a)/2} \; ,$ where the constants $$a$$ and $$b$$ establish our choice of Fourier convention1. We focus on two- and three-dimensional ($$n=2,3$$) transforms of funct