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.