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Homework Help: What is the DFT of a constant?

  1. May 3, 2013 #1
    The problem:

    What is the discrete fourier transform of a constant value?

    Example DFT{2}

    This is not my homework problem but will help me immensly in solving the actual problem.

    DFT formula:

    X[itex]_{k}[/itex] =[itex]\sum[/itex]x[n] * e[itex]^{\frac{-2\pi kn}{N}}[/itex] from n = 0 to N-1

    where N is the number of samples you can take in a 2[itex]\pi[/itex] period.
  2. jcsd
  3. May 3, 2013 #2


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    Staff Emeritus
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    Gold Member

    So x[n] = 2 for all n.

    That means you can take x[n] outside the summation, and you're left with a sum of exponential terms. Do you know how to work that out?

    Naively I would expect it to reduce to an impulse (delta function) at k = 0, or perhaps regularly repeating impulses, due to the discrete nature of the DFT. I've have to sit down and think about it some more.
  4. May 3, 2013 #3
    Ah, that helps out immensely. As it turns out it does turn into a delta function at k = 0. Thank you so much for clearing that up for me.
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