sm9_6
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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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