A method of using Simpson's rule in the DFT

The method of taking a 2N-point DFT by means of an N-point DFT is modified such that Simpson's rule replaces the trapezoidal rule in the approximation to the Fourier integral. The Simpson's rule version is compared to the trapezoidal rule version on the basis of equal upper bounds on truncation error, and it is shown that Simpson's rule has the advantage of requiring a lower sampling rate under these conditions.