—
\2-85
I
Td
:=
.1
j
:=
h f
:=
0,0.02
.•
30
H(f)
:=
1 –
cos(2’~’Td
f)
+j
sin(2
T’Td
f)
(b.
)
T
:=
X(f)
1
sin(~
T
f)
:=
T·———
~
T·f
‘l(f)
:=
H(f)
X(f)
Square
wave
T
S
ectrum
(a.)
B =
0.6
1
-~
yet)
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-1
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
~
-86
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(b.)
B = 1
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[
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hk..
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INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1-
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Com
Jd.
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alst>
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INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1
rl.
.
7T
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~
_
[1
–2
‘+
;]]
–
ata+
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n
n
(a]
fo
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300
2
~
(h)
fo
=
500
(c.)
fo
=
l….—::~—-……—-::;=——-.—-:=:——–.—=——–.
2
63
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
—>
Select
fs
fs:=
1
T
;=
1
—
is
t:=
0,0.05
••
14
n
:==
0
14
..
–
T
is
= 1
1.5
is
=
0.5
1.5
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1 2–
90
I
w~
=
‘-~
=
f)t>O
.£
1
~
‘”Z…
l.{S’ocj
—
~O\J
7S
7 TQ
1:tt
–
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I
2-91
Actual
spectrum
is
given
as
follows:
-10
f :=
10
,0.05
..
5 T
:=
1
MAGNITUDE
SPECTRUM
sin
(11′”
1
T’
f)]
The
OFT
spectrum
is
as
follows:
M
:=
6 M
N
:=
2 N=
64
k:=
0
••
N – 1
Tl
:=
12.B
W
:=
dt-
[-IN].
icfft(w)
MAGNITUDE
SPECTRUM
out
to
fs
n 1 1
f
:=-
fs
:=
–
n
Tl
dt
G5
5
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
WAVEFORM
w 1
dt
0.156
w
~
1~1
—–r-ll
o
n . – 0
..
N – 1 o t
Tl
k
2·94
n
2-86
fo
.-
5
Al
.-
4
f1
2
fo
91 . –
30
1
A2
,-
2
f2.-
5
fo
82
.-
-10
T
.-
fo
M, –5 M
N.–2
N
:::
32
k .–0
..
N – 1 1
k
Compute
the
FFT
data
points.
n
.-
0
..
N – 1 FFT
Data
Points
W
.-
J;
icfft(w)
70
67
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
(a)
See
next
screen
for
a
plot
of
the
magnitude
and
phase
spectrum.
MAGNITUDE
PHASE
I
SPECTRUM
,
8(f)
3
90
(b)
Use
(2-126)
to
get
PSD
2-95
A :=: 5
To
.-
3 T
.-
To
l
M .–6 M
fo
.-
N.–2
To
N =
64
k . – 0
..
N – l
T
dt
.––t
.-
k
dt
N k
SPEcrRUM,
I W
(f)
I
al
DenSJ.tv
Power
Spectr
5
k
Compute
the
FFT
data
points.
n : = 0
..
N – l
FIT
Data
Points
G8
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
~—+——t——-r—–r-I
since.the
waveform
is
periodic,
the
spectrum
will
contain
only
delta
funct~ons.
===>
Evaluate
the
weights
of
the
delta
functions
by
using
the
FFT
to
calculate
the
complex
Fourier
series
coefficients.
—–>
Use
(2-187)
and
(2-178)
along
with
(2-109).
c(n)
:~
if[n
~
o,:.w ,:.w ]
fen)
:=
n
–
fs
:=
1
N nN
N+n
T
dt
r:=
1.0
2-96
n:=O,
1..
N-
1
1
M:=8
fo:= 1 fs :=20 dt
:=-
T :=N·dt f
:=~
t :=n·dt
n T n
fs
fdel :=r·fo
f1
:=fo-
fdel B :=fo+fdet
Construct the Raised Cosine frequency response using the Mathcad
“if’
function.
I
Un
I
o.~
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
The Impulse Response will
now
be
calculated by
using
the Inverse FFT
and
plotted below.
h
:=
is .ICFFT(H)
N
1m
lpU
1
se
Response
2
I
2-97
I
~
l-D::.
I
+~\+)f,)
IVher~
{‘
~
~R(
-=-
9
J
o/
13
.$\,,’C.~J
~
lt
J
\”-
;:
Ilt~~
I
r=-
t.
J
t;
is
-the.
.2
dB
bo.”,o\
wiotth.
(t)
,C
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INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
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:9
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f =
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? {=.
tJ.’l-lfl(
17
,,,-f
71
INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II
1 2–
100
l-r
({)
=
/\
f.!-r;)
~
S{fJ::::
10
[So.
(;rf”4J]t-
@7<,-
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INSTRUCTOR SOLUTIONS MANUAL
(United States Edition)
Digital & Analog Comm. Systems
8th Edition, L. W. Couch, II