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Inverse dft and dft question

  1. Oct 25, 2011 #1
    How does one edit the input sequence and the results so as to be able to calculate the inverse dft with the dft algorthm?
     
  2. jcsd
  3. Oct 27, 2011 #2

    jasonRF

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    Gold Member

    if you define the DFT by:
    [tex]
    X_k = \sum_{n=0}^{N-1} x_n e^{-i 2 \pi \frac{k}{N} n} = DFT\left(x\right)_k
    [/tex]
    and it inverse DFT by
    [tex]
    x_n = \frac{1}{N} \sum_{k=0}^{N-1} X_k e^{+i 2 \pi \frac{k}{N} n} = IDFT\left(X\right)_n,
    [/tex]
    then the way to get [itex]x_n[/itex] from [itex]X_k[/itex] using a DFT would be something like,
    [tex]
    x_n = \frac{1}{N} \left(\sum_{k=0}^{N-1} X_k^* e^{-i 2 \pi \frac{k}{N} n}\right)^* = \frac{1}{N} \left( DFT \left( X^* \right) \right)_n^*
    [/tex].
    where the asterix represents conjugation. Does that make sense?

    jason
     
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