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How is this summation approx valid?

  1. Oct 22, 2009 #1
    I came across this approximation in a book. I am not sure why this approximation is valid..

    [tex]\frac{1}{N}\sum_{n=0}^{N-1}n.sin[4\pi f_o n + 2\phi] \approx 0[/tex]

    [tex]f_o[/tex] is not near 0 or 1/2

    Last edited: Oct 22, 2009
  2. jcsd
  3. Oct 22, 2009 #2
    Perhaps it's because you are averaging over a sin function, which has average 0?
  4. Oct 22, 2009 #3


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    Pretty much. Unless something funny is going on, the positives and the negatives should pretty well cancel out.

    If it is -- if you manage to get sin = 1 at each point -- you can get as high as (N - 1)/2. But for randomly-chosen f_0 and phi, I'd expect to get something pretty small. Maybe not O(N^(-1/2)), but certainly o(1).
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