In a QAM system (Fig. 4.19), the locally generated carrier has a frequency error Awo and a phase error 8; that is, the receiver carrier is cos [(c + Aw)t + 8] or sin [(@c+ Aw)t +8]. Show that the output of the upper receiver branch is m₁ (1) cos [(Aw)t +8] − m₂ (t) sin [(Aw)t +8] instead of my (1), and the output of the lower receiver branch is instead of m2 (1). m₁ (1) sin [(Aw)t +8] + m₂(1) cos [(Aw)t +8] Po(t)= m(t) cos(@t)+ m₂ sin(@t) xj (1) Low-pass filter 2 cos[(@+ Aw)t +5] m/2 2 sin [(@+ Aw)t +8] Low-pass filter X₂(1) m (1) m₂(1)

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In a QAM system (Fig. 4.19), the locally generated carrier has a frequency error Aw and a phase
error 8; that is, the receiver carrier is cos [(@wc + Aw)t + 8] or sin [(wc + Aw)t +8]. Show that
the output of the upper receiver branch is
m₁ (1) cos [(Aw)t +8] - m₂ (t) sin [(Aw)t +8]
instead of m₁ (1), and the output of the lower receiver branch is
instead of m₂ (t).
m₁ (1) sin [(Aw)t +8] + m₂(1) cos [(Aw)t +8]
POAM (t) = m(t) cos(@t) + m₂ sin(@t)
TT/2
x₁ (1)
Low-pass
filter
2 cos [(@+ Aw)t +8]
2sin [(@+ Aw)t + 8]
Low-pass
filter
X₂(1)
m₂(1)
Transcribed Image Text:In a QAM system (Fig. 4.19), the locally generated carrier has a frequency error Aw and a phase error 8; that is, the receiver carrier is cos [(@wc + Aw)t + 8] or sin [(wc + Aw)t +8]. Show that the output of the upper receiver branch is m₁ (1) cos [(Aw)t +8] - m₂ (t) sin [(Aw)t +8] instead of m₁ (1), and the output of the lower receiver branch is instead of m₂ (t). m₁ (1) sin [(Aw)t +8] + m₂(1) cos [(Aw)t +8] POAM (t) = m(t) cos(@t) + m₂ sin(@t) TT/2 x₁ (1) Low-pass filter 2 cos [(@+ Aw)t +8] 2sin [(@+ Aw)t + 8] Low-pass filter X₂(1) m₂(1)
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