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Help with digital signals (discrete fourier transform)

  1. Oct 15, 2009 #1
    I've been working on this problem for around three hours, and I'm getting nowhere... I think it may be that I don't have even the most basic grasp of the material to even get a decent start on the problem, but hopefully someone here will be able to help me...

    1. The problem statement, all variables and given/known data

    Calculate the Discrete Fourier Transform (DFT) of a 1Hz cosine wave
    sampled 4 times per second for 1 second.

    2. Relevant equations

    [tex]

    X(K) = \sum_{n=0}^{N-1} x(n)e^{-j*2*\pi*\frac{k*n}{n}}

    [/tex]

    3. The attempt at a solution
    Honestly, I'm stumped. I don't even know where to start. I'm not asking anyone to do the problem for me, but I'd be forever greatfull if someone could start me in the right direction.

    Thanks,
    Dan
     
  2. jcsd
  3. Oct 15, 2009 #2

    MATLABdude

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    Science Advisor

    Okay, start with this factoid: a 1 Hz sine wave, sampled 4 times per second for 1 second should give you 5 values (assuming you know the value at 0):
    x[0]=
    x[1]=
    x[2]=
    x[3]=
    x[4]=

    Fill in these values. Now apply the formula you listed above to find the DFT (come on, it's only 5 values!)

    X[0]=
    X[1]=
    X[2]=
    X[3]=
    X[4]=
     
  4. Oct 15, 2009 #3
    So am I right in saying
    x[0]=1
    x[1]=0
    x[2]=-1
    x[3]=0
    x[4]=1
    for a cosine wave?
     
  5. Oct 15, 2009 #4

    MATLABdude

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    Yes, that's correct. A sine wave starts at 0, however. I think the answers will differ by an imaginary number in the end (equivalent to a phase shift, if I recall correctly).
     
  6. Oct 15, 2009 #5
    Why do you find the x[n] values for a sine wave when the question is asking about a cosine wave?
     
  7. Oct 15, 2009 #6

    MATLABdude

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    Huh. I could swear your original post asked for sine. In that case, carry on!
     
  8. Oct 15, 2009 #7
    So I would plug those values into the forumula, and then add all of the outputs together?
     
  9. Oct 15, 2009 #8

    MATLABdude

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    Science Advisor

    Yup. And now?

    X[0]=
    X[1]=
    X[2]=
    X[3]=
    X[4]=
     
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