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Sum of Discrete Sinusoids

  1. Mar 13, 2014 #1
    1. The problem statement, all variables and given/known data

    Hi Everyone, I am trying to show why the given sum is zero. I am pretty sure it is zero.




    2. Relevant equations

    sin[8*[itex]\pi[/itex]*n/5]+sin[12*[itex]\pi[/itex]*n/5]

    n is an integer.

    3. The attempt at a solution

    n----sin[8*[itex]\pi[/itex]*n/5]----sin[12*[itex]\pi[/itex]*n/5]

    0 ---- 0------------------------------ 0

    1 ---- -0.9511------------------------ 0.9511

    2 ---- -0.5878------------------------ 0.5878

    3 ---- 0.5878------------------------ -0.5878

    4 ---- 0.9511------------------------ -0.9511

    5 ---- 0------------------------------- 0

    I am looking for an analytic solution thank you.
     
  2. jcsd
  3. Mar 13, 2014 #2

    Dick

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    It's because the point between those two numbers is 10*pi*n/5=2*pi*n. Enough of a hint?
     
    Last edited: Mar 13, 2014
  4. Mar 14, 2014 #3

    HallsofIvy

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    The point exactly half way between those two numbers is 2pi n.
     
  5. Mar 14, 2014 #4
    So on the unit circle the halfway point is always along the positive x-axis. And if that is halfway, the y components will always be the negative of eachother?

    Also how did you realize it was exactly half way?
     
  6. Mar 14, 2014 #5

    Dick

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    Thinking about where the points for various n lie on the unit circle is a good way.
     
  7. Mar 15, 2014 #6
    Ok, Thanks =]
     
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