sm9_6

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Problem 9.6 The signal m(t) = cos(2000πt) is transmitted by means of frequency 
modulation. If the frequency sensitivity kf is 2 kHz per volt, what is the Carson’s rule 
bandwidth of the FM signal. If the pre-detection SNR is 17 dB, calculate the post-
detection SNR. Assume the FM demodulator includes an ideal low-pass filter with 
bandwidth 3.1 kHz. 
 
Solution 
The Carson Rule bandwidth is ( ) ( ) kHzfAkB mfT 82)1(222 =+=+= . Then from 
Eq.(9.59), 
 
2 2 22
FM
post 3 3
0 0
3 3
SNR
2 2
c f fc
T
T
A k P k PA B
N W N B W
⎛ ⎞= = ⎜ ⎟⎜ ⎟⎝ ⎠
 
 
We observed that the first factor is the pre-detection SNR, and we may write this as 
 
( )
2 1
FM FM 2
post pre 3
FM
pre
3 2SNR SNR 8
3.1
SNR 1.61
~ 19.2 dB
⎛ ⎞⋅⎜ ⎟= ⎜ ⎟⎝ ⎠
= × 
 
(There is an error in the answer given in the text.) 
 
 
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