. For each of the signals in (a)-(g) below, determine which of the properties (1)-(6) listed here is satisfied by its Fourier transform. Compute as little as possible; instead invoke transform properties as necessary. (1) Re{X(e)} = 0. (2) 3m{X(e)} = 0. (3) There exists a real a such that eja X(e) is real. (4) X(e) ds = 0. (5) X(e) is periodic. (6) X(e)|₁2-0 =0. (a) x[n] in Figure P1.9-1. (b) x[n] in Figure P1.9-2. (c) x[n] in Figure P1.9-3. (d) x[n] in Figure P1.9-4. (e) x[n] = ()" u[n]. (f) x[n] = 8[n (g) x[n] = 8[n 1] + 8[n+2]. 1] +8[n+1]. -10 -2-10 1 2 x[n] 1 (a) Figure P1.9-1 x[n] 3 4 5 2 (b) Figure P1.9-2 x[n] 2 -1 0 -1 (c) Figure P1.9-3 A (d) Figure P1.9-4 11 *** www .. ....... 0 11
. For each of the signals in (a)-(g) below, determine which of the properties (1)-(6) listed here is satisfied by its Fourier transform. Compute as little as possible; instead invoke transform properties as necessary. (1) Re{X(e)} = 0. (2) 3m{X(e)} = 0. (3) There exists a real a such that eja X(e) is real. (4) X(e) ds = 0. (5) X(e) is periodic. (6) X(e)|₁2-0 =0. (a) x[n] in Figure P1.9-1. (b) x[n] in Figure P1.9-2. (c) x[n] in Figure P1.9-3. (d) x[n] in Figure P1.9-4. (e) x[n] = ()" u[n]. (f) x[n] = 8[n (g) x[n] = 8[n 1] + 8[n+2]. 1] +8[n+1]. -10 -2-10 1 2 x[n] 1 (a) Figure P1.9-1 x[n] 3 4 5 2 (b) Figure P1.9-2 x[n] 2 -1 0 -1 (c) Figure P1.9-3 A (d) Figure P1.9-4 11 *** www .. ....... 0 11
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 1.9 (a,c,d only) (Properties of DTFT)
..
![1.9. For each of the signals in (a)-(g) below, determine which of the properties
(1)-(6) listed here is satisfied by its Fourier transform. Compute as little as
possible; instead invoke transform properties as necessary.
(1) Re{X(e)} = 0.
(2) 3m{X(e)} = 0.
(3) There exists a real a such that ejaX(e) is real.
(4)
X(ei) d = 0.
(5) X(e) is periodic.
(6) X(e)|-0 =0.
(a) x[n] in Figure P1.9-1.
(b) x[n] in Figure P1.9-2.
(c) x[n] in Figure P1.9-3.
(d) x[n] in Figure P1.9-4.
(e) x[n] = (+)" u[n].
(f) x[n] = 8[n
(g) x[n] = 8[n
1] + [n+2].
1] + 8[n+ 1].
-2
x[n]
-1 0 1 2 3 4 5
Figure P1.9-1
x[n]
stopstajalopolopoli
2
(b)
-10
Figure P1.9-2
x[n]
2₁
0
-1
(c)
Figure P1.9-3
x[n]
---lappolytappelen,
0
(d)
Figure P1.9-4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9ae494b-0c93-4c1c-b8b9-6bc9a50e90cb%2F36587529-994c-495b-ab43-258ee3838221%2Fy3lmwbb_processed.png&w=3840&q=75)
Transcribed Image Text:1.9. For each of the signals in (a)-(g) below, determine which of the properties
(1)-(6) listed here is satisfied by its Fourier transform. Compute as little as
possible; instead invoke transform properties as necessary.
(1) Re{X(e)} = 0.
(2) 3m{X(e)} = 0.
(3) There exists a real a such that ejaX(e) is real.
(4)
X(ei) d = 0.
(5) X(e) is periodic.
(6) X(e)|-0 =0.
(a) x[n] in Figure P1.9-1.
(b) x[n] in Figure P1.9-2.
(c) x[n] in Figure P1.9-3.
(d) x[n] in Figure P1.9-4.
(e) x[n] = (+)" u[n].
(f) x[n] = 8[n
(g) x[n] = 8[n
1] + [n+2].
1] + 8[n+ 1].
-2
x[n]
-1 0 1 2 3 4 5
Figure P1.9-1
x[n]
stopstajalopolopoli
2
(b)
-10
Figure P1.9-2
x[n]
2₁
0
-1
(c)
Figure P1.9-3
x[n]
---lappolytappelen,
0
(d)
Figure P1.9-4
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