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Math Help - Period of signal

  1. #1
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    Period of signal

    Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

    given that x(t) = cos(600\pi t) and m(t) = 4 + 3cos(20\pi t) what is the period (if any) of the resulting signal

    Also the signal  x(t) = 10cos(600\pi t + \frac{\pi}{3}) + 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t) whats the period of the signal

    Im not sure how to calculate the period when theres more than one sinusoid wave

    Any help most appreciated
    Last edited by jordanrs; October 22nd 2010 at 03:47 AM. Reason: missed a symbol
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jordanrs View Post
    Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid



    Also the signal  x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t) whats the period of the signal

    Im not sure how to calculate the period when theres more than one sinusoid wave

    Any help most appreciated
    First question snipped as it not complete.

    The product of two sinusoids has sinusoidal components at the sum and diffrence frequencies. This for some amplitudes (non-zero) and phases is:

    x(t)=A\sin(300\pi t+\phi_1)+B\sin(1500\pi t+\phi_2)

    and since the larger period is an integer multiple of the smaller the final period is 1/150 s

    CB
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  3. #3
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    Quote Originally Posted by jordanrs View Post
    Stuck on the following problem, aint sure how to work out the signal of a composed sinusoid

    given that x(t) = cos(600\pi t) and m(t) = 4 + 3cos(20\pi t) what is the period (if any) of the resulting signal

    Also the signal  x(t) = 10cos(600\pi t + \frac{\pi}{3}) 6cos(900\pi t - \frac{\pi}{4}) - 4cos(1500\pi t) whats the period of the signal

    Im not sure how to calculate the period when theres more than one sinusoid wave

    Any help most appreciated
    cheers for your reply, the first part should have read

    when y(t) = x(t)m(t) and x(t) = cos(600\pi t) and m(t) = 4 + 3cos(20\pi t) what is the resulting period of (y(t))

    also i still dont get how to calculate the periodm i dont see where you got 1/150 s from
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by jordanrs View Post
    cheers for your reply, the first part should have read

    when y(t) = x(t)m(t) and x(t) = cos(600\pi t) and m(t) = 4 + 3cos(20\pi t) what is the resulting period of (y(t))

    also i still dont get how to calculate the periodm i dont see where you got 1/150 s from
    You decompose the signal into a sum of sinusoids, then the period is the lcm of the individual periods of the components.

    CB
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