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I'm trying to solve a problem regarding communication and I'm stuck. The questions asked me to find the maximum frequency deviation are usually written in cos or sin wave. But this question isn't, so I'm baffled and don't know how to start. enter image description here

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What you need to know is how phase and frequency are related for a signal of the form $x(t)=\cos(\phi(t))$:

$$f(t)=\frac{1}{2\pi}\frac{d\phi(t)}{dt}\tag{1}$$

If $\phi(t)=2\pi f_ct$, then from $(1)$ we get $f(t)=f_c$, which is a result we usually don't need to think about. However, for a more general phase function $\phi(t)$, we can use Eq. $(1)$ to determine the (time varying) frequency $f(t)$.

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  • $\begingroup$ Thank you for your reply. I did try to write my phi(t). As you can see in the graph. phi(t) has two separate equations. One from t=0 to 10^(-3), the other from t = 10^(-3) to 3*10^(-3). When I differentiate them, I get 500pi - 250pi, these two terms were from two separate equations, respectively. Since the question is asking ''maximum'' frequency deviation, I'm wondering if I should consider the -250pi, because it makes the answer smaller. $\endgroup$ Commented Nov 26, 2022 at 10:49
  • $\begingroup$ @wannastudycommunication: The frequency deviation is $\Delta f=|f(t)-f_c|$. Just determine the maximum and you're done. $\endgroup$
    – Matt L.
    Commented Nov 26, 2022 at 11:13
  • $\begingroup$ Thank you for the help! I think I should pick 500pi as my answer (since it's the maximum). How about finding the maximum phase deviation. If I don't misunderstand, for a signal s(t)=[cos⁡(Bt)+C sin⁡(2πft)], the maximum phase deviation would be C. But in this case I can't convert the whole composite signal in (b) into a cos containing a sin. $\endgroup$ Commented Nov 26, 2022 at 14:37

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