8 Communication systems
8.1 Complex Exponential and Sinusoidal
Amplitude Modulation
Modulating system model:
8,Communication Systems
x(t)
c(t)
y(t)=x(t)c(t)
x(t) --- modulating signal
c(t) --- Carrier signal
8 Communication systems
8.1.1 Amplitude Modulation with Complex
Exponential Carrier
Exponential carrier:
For convenience,let?c=0,so
)()( cc tjetc
tj cetc)(
Output signal(modulated signal),tj
cetxty?)()(?
)()(
)(2)(
)(*)(
2
1
)(
c
c
jjXjY
jC
jCjXjY





(1) Modulation Theory
8 Communication systems
8 Communication systems
ttjxttx
etxty
cc
tj c

s in)(c o s)(
)()(

(1) Implementation
8 Communication systems
8.1.2 Amplitude Modulation with Sinusoidal signal
For convenience,choose?c=0,so
ttxtctxty c?c o s)()()()(
)(
2
1
)(
2
1
)(
)()()(
)(*)(
2
1
)(
cc
cc
jjXjjXjY
jC
jCjXjY





8 Communication systems
8 Communication systems
8 Communication systems
8.2 Demodulation for Sinusoidal AM
8.2.1 Synchronous demodulation
(1) Demodulation process
8 Communication systems
)2(41)2(41)(21)( cc jjXjjXjXjW
In frequency domain:
ttxtx
ttx
tctytw
c
c
2c o s)(
2
1
)(
2
1
c o s)(
)()()(
2

In time domain:
Expected signal,)()(?jWortx
8 Communication systems
8 Communication systems
(2) Synchronous problem
8 Communication systems
Time domain:
)2c o s ()(
2
1
)c o s ()(
2
1
)c o s ()c o s ()(
)c o s ()()(
ccccc
cccc
cc
ttxtx
tttx
ttytw






The output of lowpass filter,)c o s ()( cctx
Ideal output,x(t) )( d e s ir e dis
cc
When,it is referred to as synchronous
demodulation.
cc
8 Communication systems
8.2.2 Asynchronous demodulation
Amplitude-modulated signal:
tAtxty c?c o s])([)(
8 Communication systems
8 Communication systems
Problem,8.1 8.3 8.22 8.28