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Fourier transforms

  1. Mar 29, 2010 #1
    1. The problem statement, all variables and given/known data
    Hello: I have a say N = 7 vector. Say I know that it's DFT is X = [X[0] X[1] ... X[6]]
    I am wondering if there is any way that I can find the sum of:
    x[1] - x[2] + x[3] - x[4] + x[5] - x[6]?
    Since N = odd, I can't use the trick with N/2 = pi as a frequency. Thanks so much.
    My signal x{n] is real, but I really can't see any relation between the entries of X and x.
     
  2. jcsd
  3. Mar 31, 2010 #2

    marcusl

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    Science Advisor
    Gold Member

    You could express your modified sequence as the product of the sequence x times a square wave:

    [tex]x'_n=(-1)^n x_n, [/tex] with n=0, 1, ...

    Try taking it from there. Hint: what is the Fourier transform of a product of two functions?
     
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