sm9_16

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Problem 9.16 An AM receiver, operating with a sinusoidal modulating wave and 80% 
modulation, has a post-detection signal-to-noise ratio of 30 dB. What is the 
corresponding pre-detection signal-to-noise ratio? 
 
Solution 
We are given that ka = 0.80, and for sinusoidal modulation P = 0.5. A post-detection SNR 
of 30 dB corresponds to an absolute SNR of 1000. From Eq.(9.30), 
 
5.0)8.0(
2
1000
2
2
0
2
0
22
WN
A
WN
PkASNR
c
aCAM
post
=
=
 
 
Re-arranging this equation, we obtain 
3125
2 0
2
=
WN
Ac 
 
From Eq. (9.26 ) the pre-detection SNR is given by 
 ( )
( )
( )
5.2062
5.0)8.0(1
2
3125
1
)2(2
2
1
2
2
0
2
0
22
=
+=
+=
+=
Pk
WN
A
BN
PkASNR
a
c
T
aCAM
pre
 
 
where we have assumed that BT = 2W. This pre-detection SNR is equivalent to 
approximately 36 dB. 
 
 
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