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Homework Help: Fourier Transforms

  1. Mar 27, 2005 #1

    mcfetridges

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    I am having a little trouble. I am asked to evaluate the fourier transform of a periodic train of triangle shaped pulses. Then I have to evaluate the power spectral density. Now it is very easy to find the fourier transform of one of the triangles, but what do I do when it is periodic? Do I have evaluate the signal with the fourier series and using the relationships between the magnitude of Dn to find the mag. of F(w) and then get the spectral density?
     
    mcfetridges, Mar 27, 2005
  2. jcsd
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  3. Mar 28, 2005 #2

    LeBrad

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    A train of triangles could also be written as a single triangle convolved with an impulse train. Do you know what convolution in the time domain becomes in the frequency domain?
     
    LeBrad, Mar 28, 2005
  4. Mar 28, 2005 #3

    mcfetridges

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    Ya in the frequency domain it becomes autocorrelation. But is that the only way?
     
    mcfetridges, Mar 28, 2005
  5. Mar 28, 2005 #4

    LeBrad

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    If autocorrelation means multiplication, then yes, that is correct. Convolution in one domain goes to multiplication in the other.

    Maybe there's an easier way to do it, but I don't think this way is that hard.

    A triangle is a box convolved with another box. A box is a sinc(x) function, so a triangle would be sinc(x)^2.

    The Fourier transform of an impulse train is another impulse train, but with different spacing and weights.

    Multiply the two together, and you get a sampled sinc(x)^2 function. Yes?
     
    LeBrad, Mar 28, 2005
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