Comparison of the DFT and FFT via Matrices
<text> The purpose of this article is to illustrate the differences of the Discrete Fourier Transform (DFT) versus the Fast Fourier Transform (FFT) as well as provide an alternative . Please note, the following explanation of the FFT will use the "divide and conquer" method. </text>
To start, we will define the DFT as,
$ X[k] = \sum_{n=0}^{N-1} x[n] e^{-j2{\pi}kn/N} $
