Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Please solve 3.54 (e) step by step original solution
![326
(e) X(jw) as depicted in Figure P3.55(b).
(f) X(jw) as depicted in Figure P3.55(c).
-2
x(1)
-1
1
0
(a)
FIGURE P3.54
2
-2
t
IX(jw)|
1
0
arg{X(jw))
CHAPTER 3 FOURIER REPRESENTATIONS OF SIGNALS AND LINEAR TIME-INVARIANT SYSTEMS
2
2
x(t)
0
(b)
343
2
of 820
FIGURE P3.53
(c)
3.56 Determine the appropriate Fourier representations
of the following time-domain signals, using the defin-
ing equations:
(a) x(t) = ecos(2πt)u(t)
(b) x[n]
=
(cos(ion) + jsin(n), |-|< 10
0,
otherwise
(c) x[n] as depicted in Figure P3.56(a).
(d) x(t) = e¹tu(-t + 2)
(e) x(t) = sin(2πt)|
(f) x[n] as depicted in Figure P3.56(b).
(g) x(t) as depicted in Figure P3.56(c).
3.57 Determine the time-domain signal corresponding to
each of the following frequency-domain representa-
tions:
(a) X[k]:
=
e-kw/2, k < 10
0, otherwise
Fundamental period of time domain signal is
T = 1.
7
K](https://content.bartleby.com/qna-images/question/5d71aeb7-90dd-4475-8de7-819e322d230f/ce036fbd-c85f-447e-aaf7-b738db4db322/6cv6hbb_processed.jpeg)
Transcribed Image Text:326
(e) X(jw) as depicted in Figure P3.55(b).
(f) X(jw) as depicted in Figure P3.55(c).
-2
x(1)
-1
1
0
(a)
FIGURE P3.54
2
-2
t
IX(jw)|
1
0
arg{X(jw))
CHAPTER 3 FOURIER REPRESENTATIONS OF SIGNALS AND LINEAR TIME-INVARIANT SYSTEMS
2
2
x(t)
0
(b)
343
2
of 820
FIGURE P3.53
(c)
3.56 Determine the appropriate Fourier representations
of the following time-domain signals, using the defin-
ing equations:
(a) x(t) = ecos(2πt)u(t)
(b) x[n]
=
(cos(ion) + jsin(n), |-|< 10
0,
otherwise
(c) x[n] as depicted in Figure P3.56(a).
(d) x(t) = e¹tu(-t + 2)
(e) x(t) = sin(2πt)|
(f) x[n] as depicted in Figure P3.56(b).
(g) x(t) as depicted in Figure P3.56(c).
3.57 Determine the time-domain signal corresponding to
each of the following frequency-domain representa-
tions:
(a) X[k]:
=
e-kw/2, k < 10
0, otherwise
Fundamental period of time domain signal is
T = 1.
7
K
Transcribed Image Text:FIGURE P3.52
3.53 Use the equation describing the DTFT representa-
tion to determine the time-domain signals corre-
sponding to the following DTFTs:
(a) X(e) = cos(20) +isin(20)
(b) X(e) = sin(n) + cos().
(c) |X(e) =
[1, π/4 < | < 3π/4,
otherwise
arg{X(e)}:
= -40
(d) X(e) as depicted in Figure P3.53(a).
(e) X(e) as depicted in Figure P3.53(b).
(f) X(e) as depicted in Figure P3.53(c).
3.54 Use the defining equation for the FT to evaluate the
frequency-domain representations of the following
signals:
(a) x(t) = eu(t - 3)
(b) x(t) = e
(c) x(t) = te 'u(t)
(d) x(t) = m-am8(tm), al < 1
(e) x(t) as depicted in Figure P3.54(a).
(f) x(t) as depicted in Figure P3.54(b).
3.55 Use the equation describing the FT representation to
determine the time-domain signals corresponding to
the following FTs:
(a) X(jw) =
(b) X(jw) eu (w)
=
(c) X(jw) = elad
(d) X(jw) as depicted in Figure P3.55(a).
(e) X(jw) as depicted in Figure P3.55(b).
(f) X(jw) as depicted in Figure P3.55(c).
(cos(2w), w <
0,
otherwise
Y
-2π
...
-2π
-2π
-2π
X(e)
FIGURE P3.53
IX(e)|
MMM..
m/2
-T-TT/2
0
(a)
0
arg(X(e)}
2π-
未
-T
0
-2π
-#-#12
sin (52)
(b)
IX(e)|
1
-"/2
-TT
0
arg{X(e))
0
T
TT/2
TT/2 म
(c)
2π
т
2π
fi
2π
3π
+9
3π
2π
2T
Q
Ω
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