# The signal m(t) = cos(ωmt) is SSB (single side-band) modulated with a carrier cos(ωct) to get s(t). The signal obtained by passing s(t) through an ide

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The signal m(t) = cos(ωmt) is SSB (single side-band) modulated with a carrier cos(ωct) to get s(t). The signal obtained by passing s(t) through an ideal envelope detector is
1. cos(ωmt)
2. sin(ωmt)
3. cos(ωmt) + sin(ωmt)
4. 1

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Correct Answer - Option 4 : 1

1) General equation of SSB modulated wave:

$s\left( t \right) = \frac{{{A_C}{A_m}}}{2}cos\;2\pi \left( {{f_c} + {f_m}} \right)t$

2) Output of envelope detector to signal

Acos ωct → A

Application:

Equation of SSB modulated signal

Ac = Am = 1

$s\left( t \right) = \frac{1}{2}\cos \left( {{\omega _c} \pm {\omega _n}} \right)t$

the output of envelope detector = ½

The output of the envelope detector is a constant voltage signal

Hence option (d) which represents a constant voltage is correct.