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Fourier Series of cos4t + sin8t

  1. May 16, 2012 #1
    Hi everyone,

    So I was trying to calcule the Fourier Series of x(t) = cos4t + sin8t, but I'm a little bit confused. What would be ω0 in this case since I have a combination of two functions with different frequencies?

    Thank you in advance.
     
  2. jcsd
  3. May 16, 2012 #2

    HallsofIvy

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    I don't know what you mean by [itex]\omega_0[/itex] here. A Fourier series is a sum
    [tex]\sum_{n=0}^\infty A_n sin(nt)+ B_n cos(nt)[/tex]
    Here, obviously [itex]A_8= 1[/itex], [itex]B_4= 1[/itex] and all other coefficients are 0.
     
  4. May 16, 2012 #3
    I thought the series was the sum of An*cos(nw0t) + Bn*sen(nw0t)
     
  5. May 16, 2012 #4
    Typically fourier series are presented as HallsofIvy posted. However, there's no reason not to include a frequency term [itex]\omega_0[/itex]. This can simplify some expressions, and you are free to choose any [itex]\omega_0[/itex] you like. It's important to remember that any choice of [itex]\omega_0[/itex] changes the periodicity to [itex]\frac{2\pi}{\omega_0}[/itex].

    For your example, it's clearly best to choose [itex]\omega_0=1[/itex]
     
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