(New page: == == Discrete Fourier Transform == == == definition == Let X[n] be a DT signal with period N DFT <math> X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N}</math> IDFT <math> x [n] = (...) |
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| − | + | === Discrete Fourier Transform === | |
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Let X[n] be a DT signal with period N | Let X[n] be a DT signal with period N | ||
| − | DFT | + | DFT |
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<math> X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N}</math> | <math> X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N}</math> | ||
IDFT | IDFT | ||
| + | |||
<math> x [n] = (1/N) \sum_{k=0}^{N-1} X[k].e^{J.2pi.kn/N}</math> | <math> x [n] = (1/N) \sum_{k=0}^{N-1} X[k].e^{J.2pi.kn/N}</math> | ||
== Derivation == | == Derivation == | ||
Revision as of 22:07, 22 September 2009
Discrete Fourier Transform
definition
Let X[n] be a DT signal with period N
DFT
$ X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N} $
IDFT
$ x [n] = (1/N) \sum_{k=0}^{N-1} X[k].e^{J.2pi.kn/N} $
