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== DFT ( Discrete Fourier Transform ) == | == DFT ( Discrete Fourier Transform ) == | ||
| + | The DFT is a finite sum, so it can be computed using a computer. Used for discrete, time-limited signals, or discrete periodic signals. | ||
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'''DFT''' | '''DFT''' | ||
| − | *<math>X(k) = \sum_{n=0}^{N-1}{x[n]e^{- | + | *<math>X(k) = \sum_{n=0}^{N-1}{x[n]e^{-j \frac{2{\pi}}{N}kn}}, k = 0, 1, 2, ..., N-1</math> |
'''Inverse DFT (IDFT)''' | '''Inverse DFT (IDFT)''' | ||
| − | *<math>x[n] = \frac{1}{N}\sum_{k=0}^{N-1}{X(k)e^{ | + | *<math>x[n] = \frac{1}{N}\sum_{k=0}^{N-1}{X(k)e^{j \frac{2{\pi}}{N}kn}}, n = 0, 1, 2, ..., N-1</math> |
[[ECE438_(BoutinFall2009)|Back to ECE438 course page]] | [[ECE438_(BoutinFall2009)|Back to ECE438 course page]] | ||
Revision as of 10:01, 25 September 2009
DFT ( Discrete Fourier Transform )
The DFT is a finite sum, so it can be computed using a computer. Used for discrete, time-limited signals, or discrete periodic signals.
Definition
DFT
- $ X(k) = \sum_{n=0}^{N-1}{x[n]e^{-j \frac{2{\pi}}{N}kn}}, k = 0, 1, 2, ..., N-1 $
Inverse DFT (IDFT)
- $ x[n] = \frac{1}{N}\sum_{k=0}^{N-1}{X(k)e^{j \frac{2{\pi}}{N}kn}}, n = 0, 1, 2, ..., N-1 $
