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Sum of sinosoids that can be a Fourier Series expansion

  1. Aug 26, 2016 #1
    1. The problem statement, all variables and given/known data
    I was given a problem with a list of sums of sinusoidal signals, such as
    Example that I made up: x(t)=cos(t)+5sin(5*t). The problem asks if a given expression could be a Fourier expansion.
    2. Relevant equations



    3. The attempt at a solution
    My guess is that it has something to do with 5 being an integer multiple of 1.
     
  2. jcsd
  3. Aug 26, 2016 #2

    LCKurtz

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    Can you write your sum as$$
    \cos t + 5\sin(5t) = a_0 + \sum_{n=1}^\infty \left ( a_n\cos(\frac {n\pi t} p) + b_n\sin(\frac {n\pi t} p)\right )$$
    by choosing certain values for the ##a_n,~b_n,~p##? Hint: lots of them can be ##0##.
     
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