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Math Help - Complex Fourier

  1. #1
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    Thumbs down Complex Fourier

    hey

    complex to say atleast.

    im stuck with the exercise beneath. i have to work this out by monday but i need some help, i don't know integration by parts that well if that is what is used to work it out and i don't quite get how can i show it graphically. im hoping someone will cheer me up and solve this with me so i have an example for in the future.

    f(t) = 0 for t ∈ [0,3]
    f(t) = 3 for t ∈ [-3,0]

    Period = 6

    "Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."

    The answer of the function should look like this

    thanks for the kind person(s) who are willing to help, it's really a blessing.

    kind regards
    kim
    Last edited by Kimmeke; January 15th 2010 at 10:52 PM.
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  2. #2
    Senior Member DeMath's Avatar
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    Quote Originally Posted by Kimmeke View Post
    hey

    complex to say atleast.

    im stuck with the exercise beneath. i have to work this out by monday but i need some help, i don't know integration by parts that well if that is what is used to work it out and i don't quite get how can i show it graphically. im hoping someone will cheer me up and solve this with me so i have an example for in the future.

    f(t) = 0 for t ∈ [0,3]
    f(t) = 3 for t ∈ [-3,0]

    Period = 6

    "Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."

    The answer of the function should look like this

    thanks for the kind person(s) who are willing to help, it's really a blessing.

    kind regards
    kim

    f(t) = \begin{cases}<br />
  3,  & \mbox{if}~~- 3 \leqslant t \leqslant 0; \\<br />
  0, & \mbox{if}\quad\quad 0 < t \leqslant 3. <br />
\end{cases}

    f(t) = \frac{3i}{2\pi}\sum\limits_{n= -\infty}^{+\infty} \frac{1 - e^{i\pi n}}{n}e^{i\tfrac{\pi nt}{3}} = \frac{3}{2} - \frac{6}{\pi}\sum\limits_{n=1}^{+\infty} \frac{1}{2n - 1}\sin\frac{(2n - 1)\pi t}{3} .


    "Work out the function and plot 2 periods of the signal, also show it graphically for a series (5 terms)."
    I think it should look that way:




    Also see the attachment (higher quality).
    Attached Thumbnails Attached Thumbnails Complex Fourier-graph-16.01.2010-.bmp  
    Last edited by DeMath; January 16th 2010 at 10:04 AM.
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