A carrier signal
Question:

A carrier signal $\mathrm{C}(\mathrm{t})=25 \sin \left(2.512 \times 10^{10} \mathrm{t}\right)$ is amplitude modulated by a message signal $\mathrm{m}(\mathrm{t})=5 \sin \left(1.57 \times 10^{8} \mathrm{t}\right)$ and transmitted through an antenna. What will be the bandwidth of the modulated signal?

  1. (1) $8 \mathrm{GHz}$

  2. (2) $2.01 \mathrm{GHz}$

  3. (3) $1987.5 \mathrm{MHz}$

  4. (4) $50 \mathrm{MHz}$


Correct Option: , 4

Solution:

(4)

Band width $=2 \mathrm{f}_{\mathrm{m}}$

$\omega_{\mathrm{m}}=1.57 \times 10^{8}=2 \pi \mathrm{f}_{\mathrm{m}}$

$\mathrm{BW}=2 \mathrm{f}_{\mathrm{m}}=\frac{10^{8}}{2} \mathrm{~Hz}=50 \mathrm{MHz}$

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