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Math Help - What is the mathematical bandwidth of the signal?

  1. #1
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    What is the mathematical bandwidth of the signal?

    Given a signal is angle modulate and is:

    Xc(t)=10cos(2 pi 10^8 t + 200cos 2 pi 10^3 t)


    Find what is the bandwith?
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  2. #2
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    Quote Originally Posted by orendacl View Post
    Given a signal is angle modulate and is:

    Xc(t)=10cos(2 pi 10^8 t + 200cos 2 pi 10^3 t)


    Find what is the bandwith?
    The analytic representation of this signal is:

    s(t)=10\exp(\text{i}[2\pi f_0 t + 200 \cos(2 \pi f_1 t)])

    so the instantaneous phase is:

     <br />
\phi(t)=2\pi f_0 t + 200 \cos(2 \pi f_1 t)<br />

    and the instantaneous frequency is:

     <br />
f(t)=\frac{1}{2\pi}~\frac{\partial}{\partial t}\phi(t)= f_0 + 200 f_1 \sin(2 \pi f_1 t)<br />

    and the bandwidth is therefor the difference between the higest and lowest instataneous frequencies:

     <br />
{\bf{B}}=400 \pi f_1<br />

    CB
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