1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    cepheid

    User Avatar
    Staff Emeritus
    Science Advisor
    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: What is the DFT of a constant?
  1. DFT of sinc (Replies: 3)

  2. DFT Properties (Replies: 1)

Loading...