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'''Comparison of the DFT and FFT via Matrices''' | '''Comparison of the DFT and FFT via Matrices''' | ||
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| + | <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, | To start, we will define the DFT as, | ||
<math>X[k] = \sum_{n=0}^{N-1} x[n] e^{-j2{\pi}kn/N} </math> | <math>X[k] = \sum_{n=0}^{N-1} x[n] e^{-j2{\pi}kn/N} </math> | ||
Revision as of 09:54, 26 October 2013
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} $
