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(A) In amplitude modulation, the sideband frequencies are given by $f_1 = f_c - f_m$ and $f_2 = f_c + f_m$.Adding these two equations: $f_1 + f_2 = (f

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$\left|\frac{f_1+f_2}{f_2-f_1}\right|$

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(A) In amplitude modulation, the sideband frequencies are given by $f_1 = f_c - f_m$ and $f_2 = f_c + f_m$.Adding these two equations: $f_1 + f_2 = (f_c - f_m) + (f_c + f_m) = 2f_c$, which implies $f_c = \frac{f_1 + f_2}{2}$.Subtracting the first from the second: $f_2 - f_1 = (f_c + f_m) - (f_c - f_m) = 2f_m$, which implies $f_m = \frac{f_2 - f_1}{2}$.Therefore, the ratio $\frac{f_c}{f_m} = \frac{(f_1 + f_2)/2}{(f_2 - f_1)/2} = \frac{f_1 + f_2}{f_2 - f_1}$.Taking the absolute value to ensure a positive ratio, we get $\left|\frac{f_1+f_2}{f_2-f_1}\right|$.

$A$ message signal of frequency $f_m$ is used to modulate a carrier of frequency $f_c$. If the sidebands are $f_1$ and $f_2$, then the ratio $\frac{f_c}{f_m}$ is:

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