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A speech signal of $3 \mathrm{kHz}$ is used to modulate a carrier signal of frequency $1 \mathrm{MHz}$, using amplitude modulation. The freqeuncies of the side bands will be
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The correct answer is:
$1.003 \mathrm{MHz}$ and $0.997 \mathrm{MHz}$
$1.003 \mathrm{MHz}$ and $0.997 \mathrm{MHz}$
Given, frequency of carrier signal is
$$
\omega_{\mathrm{c}}=1 \mathrm{MHz}
$$
frequency of speech signal $W_{\mathrm{m}}=3 \mathrm{kHz}$
$$
=3 \times 10^{-3} \mathrm{MHz}
$$
$\omega_{\mathrm{m}}=0.003 \mathrm{MHz}$
So frequency of side bands are :
$$
\begin{aligned}
&=\left(\omega_{\mathrm{c}} \pm \omega_{\mathrm{m}}\right)=(1 \pm 0.003) \\
&=1.003 \mathrm{MHz} \text { and } 0.997 \mathrm{MHz}
\end{aligned}
$$
$$
\omega_{\mathrm{c}}=1 \mathrm{MHz}
$$
frequency of speech signal $W_{\mathrm{m}}=3 \mathrm{kHz}$
$$
=3 \times 10^{-3} \mathrm{MHz}
$$
$\omega_{\mathrm{m}}=0.003 \mathrm{MHz}$
So frequency of side bands are :
$$
\begin{aligned}
&=\left(\omega_{\mathrm{c}} \pm \omega_{\mathrm{m}}\right)=(1 \pm 0.003) \\
&=1.003 \mathrm{MHz} \text { and } 0.997 \mathrm{MHz}
\end{aligned}
$$
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