  The Fourier transform is approximated over a finite domain using a Riemann
sum. This Riemann sum is then expressed in terms of the discrete Fourier
transform, which allows the sum to be computed with a fast Fourier transform
algorithm more rapidly than via a direct matrix multiplication. Advantages and
limitations of using this method to approximate the Fourier transform are
discussed, and prototypical MATLAB codes implementing the method are presented.
