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# sm9_6

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```Problem 9.6 The signal m(t) = cos(2000\u3c0t) is transmitted by means of frequency
modulation. If the frequency sensitivity kf is 2 kHz per volt, what is the Carson\u2019s 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
\u239b \u239e= = \u239c \u239f\u239c \u239f\u239d \u23a0

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
\u239b \u239e\u22c5\u239c \u239f= \u239c \u239f\u239d \u23a0
= ×

(There is an error in the answer given in the text.)

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