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Math Help - Fourier series - addition of cosine and sine of different frequencies

  1. #1
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    Fourier series - addition of cosine and sine of different frequencies

    I need to find the Fouier series of the following:

    f(t) = cos(4t) + sin(6t)

    I know what they are individually, but for both of them added together I get a period of (pi / 2) / (pi / 3) = 3 / 2 so the period is 6,,, correct? The fourier series by themselves are just cos(4t) and sin(6t) repectively. Do you just place this expression in the formulae with T = 6? That's a lot of messy math. Any help on how to do this would be very much appreciated.

    In addition, when I graph this on Matlab the period is smaller than 6. It looks a little bigger then 3. Any hints on what's going on?

    Thanks
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  2. #2
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    reply to first answer

    OK,, I've been taught, maybe the wrong way, that in order to find a common period of two sums such as cos(4t) + sin(6t) you do the following:

    Find periods: 2pi / 4 = pi / 2 -- This is first period T1

    Next,, 2pi / 6 = pi / 3 -- This is second period T2

    Now T1 / T2 must be rational so (pi / 2) * (3 / pi) = 3 / 2 which is rational. Now find LCM(3, 2) which is 6.

    What is wrong with this? Why would a graph show it is pi which is an irrational number?
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  3. #3
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    Quote Originally Posted by afried01 View Post
    OK,, I've been taught, maybe the wrong way, that in order to find a common period of two sums such as cos(4t) + sin(6t) you do the following:

    Find periods: 2pi / 4 = pi / 2 -- This is first period T1

    Next,, 2pi / 6 = pi / 3 -- This is second period T2

    Now T1 / T2 must be rational so (pi / 2) * (3 / pi) = 3 / 2 which is rational. Now find LCM(3, 2) which is 6.

    What is wrong with this? Why would a graph show it is pi which is an irrational number?
    Except the period has to be an integer multiple of $$ \pi (and that integer is the \gcd(2,3)=1)

    CB
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