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# sm9_13

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```Problem 9.13 Assume a message signal m(t) has power spectral density

\u23aa\u23a9
\u23aa\u23a8
\u23a7 \u2264=
otherwise0
)( WfW
f
afSM

where a and W are constants. Find the expression for post-detection SNR of the receiver
when
(a) The signal is transmitted by DSB-SC.
(b) The signal is transmitted by envelope modulation with ka = 0.3.
(c) The signal is transmitted with frequency modulation with kf = 500 hertz per
volt.
Assume that white Gaussian noise of zero mean and power spectral density N0/2 is added
to the signal at the receiver input.

Solution

(a) with DSB-SC modulation and detection, the post-detection SNR is given by

WN
PASNR cDSB
0
2
2
=

For the given message spectrum, the power is

aW
df
W
fa
dffSP
W
M
=
=
=
\u222b
\u222b\u221e
\u221e\u2212
0
2
)(

where we have used the even-symmetry of the message spectrum on the second line.
Consequently, the post-detection SNR is

0
2
2N
aASNR cDSB =

(b) for envelope detection with ka = 0.3, the post-detection SNR is

Continued on next slide
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to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
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Problem 9.13 continued
2 2
AM
0
2
2
0
2
0
SNR
2
2
0.09
2
c a
c
a
c
A k P
N W
A a k
N
A a
N
=
=
=

(c) for frequency modulation and detection with kf = 500 Hz/V, the post-detection
SNR is

2
0
2
3
0
22
FM
3
2
2
3
SNR
\u239f\u239f\u23a0
\u239e
\u239c\u239c\u239d
\u239b=
=
W
k
N
aA
WN
PkA
fc
fc

Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.```