DFT scaling property

Discussion in 'Math' started by Georacer, Apr 2, 2013.

  1. Georacer

    Thread Starter Moderator

    Nov 25, 2009
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    Hello everybody,

    In the context of DFT, I am given an 8-point signal x[n] with the 8-point DFT of X[k].

    What is the IDFT of the sequence X[2k], for k=0-3?
    I 've been trying to find a formal answer specifically for the DFT all day but to no avail.

    Can you point me to a resource or provide an answer? A proof would be even better.

    Thanks in advance.
     
    Last edited: Apr 2, 2013
  2. t06afre

    AAC Fanatic!

    May 11, 2009
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    Frequency or amplitude?
     
  3. Georacer

    Thread Starter Moderator

    Nov 25, 2009
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    The starting signal x[n] is real.
    X[k] is the complex-valued DFT.

    In short, I 'm interested in general, complex quantities.
     
  4. Georacer

    Thread Starter Moderator

    Nov 25, 2009
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    I got the answer after all.

    When downsampling the frequency by two, the time signal is wrapped in a new periodic signal of half the period and aliasing happens.

    Thus, if P[k]=X[2k], k=0,...,3 then
    p[n]=[x[0]+x[4] x[1]+x[5] x[2]+x[6] x[3]+x[7]]

    It dawned on me after reading the problem solution for two days.
     
  5. t06afre

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  6. Georacer

    Thread Starter Moderator

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    This was a uni course theoretical question, so there was no room for experimentation.

    The question was:
    You have x[n]=[ 2 -1 1 0 3 -2 3 -3]
    If X[k] is the 8-point DFT of x[n], what is r[n], if R[k]=|X[2k]|^2?

    As you can see, it was a bit more complex and broad than my original question.
     
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