
\begin{abstract}
Riemann sums and counting measure are used to motivate an intuitive derivation
of the discrete Fourier transform.  Poisson summation is then used to obtain an
error estimate for the DFT with respect to the continuous Fourier transform on
the circle.  This paper fulfills a term-paper requirement for Bill Faris'
spring 2006 Real Analysis course (Math 523B).
\end{abstract}
