Problem#4: Sketch the amplitude (magnitude) spectrum and phase spectrum of the periodic signals: x(t) = 2 cos(xt) + sin(2rt) Note: you can use the FT tables. Answer: TABLE 3.1 Short Table of Fourier Transforms g(t) GỰ) g(t) GỰ) a+j2af a>0 10 sin 2rfof j0.5 [8(f +fo) – 8(f – fo)] 2 u(-t) a >0 11 (t) a – j2af 2a 2af 2 3 e-al a² + (2xf)² a>0 12 sgnt 2af 4 te-#u(t) a >0 (a +j2nf)2 n! n() z sinc (7fr) 5 reu(t) a >0 n() sine () (a +j2¤f)*+ 18 2B sinc (27 Br) п 2B 6 8(1) 19 7 1 SF) Sif – fo) 20 B sinc² (7Bt) A cos 2n fot 0.5 [8(f +fo) + 8f – fo)] 21 E 8(t – nT) fo E- 8f – nfo) fo = }
Problem#4: Sketch the amplitude (magnitude) spectrum and phase spectrum of the periodic signals: x(t) = 2 cos(xt) + sin(2rt) Note: you can use the FT tables. Answer: TABLE 3.1 Short Table of Fourier Transforms g(t) GỰ) g(t) GỰ) a+j2af a>0 10 sin 2rfof j0.5 [8(f +fo) – 8(f – fo)] 2 u(-t) a >0 11 (t) a – j2af 2a 2af 2 3 e-al a² + (2xf)² a>0 12 sgnt 2af 4 te-#u(t) a >0 (a +j2nf)2 n! n() z sinc (7fr) 5 reu(t) a >0 n() sine () (a +j2¤f)*+ 18 2B sinc (27 Br) п 2B 6 8(1) 19 7 1 SF) Sif – fo) 20 B sinc² (7Bt) A cos 2n fot 0.5 [8(f +fo) + 8f – fo)] 21 E 8(t – nT) fo E- 8f – nfo) fo = }
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Question
![Problem#4:
Sketch the amplitude (magnitude) spectrum and phase spectrum of the periodic signals:
x(t) = 2 cos(xt) + sin(2nt)
Note: you can use the FT tables.
Answer:
TABLE 3.1
Short Table of Fourier Transforms
g(1)
GF)
g(1)
GỰ)
I u(t)
a >0
10 sin 2nfof
jo.5 [8(f +fo) – 8f – fo)]
a+j2af
2 e u(-t)
a>0
I1 u(t)
1
a - j2nf
2a
3 e-all
a >0
a² + (2xf)²
12 sgn?
4 te-u(t)
a >0
(a +j2nf)?
n!
(4)
17 n
z sinc (æft)
5 re-au(t)
a >0
(a +j2nf)n+
18 2B sinc (27 Bt)
6 8(1)
2B
19 A
Sf)
sinc2
Sf – fo)
20 B sinc? (7Bt)
A
2B
cos 2nfot
0.5 [8(f +fo) + 8(f – fo)]
21 E- 8(t – nT') fo E- 8f – nfo) fo = +
Ln=-00](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fac4457bd-4c88-42ff-bf50-69f41e26f550%2F337bef16-fc5a-4289-92ec-c9401ac0b543%2Fxrjkn7m_processed.png&w=3840&q=75)
Transcribed Image Text:Problem#4:
Sketch the amplitude (magnitude) spectrum and phase spectrum of the periodic signals:
x(t) = 2 cos(xt) + sin(2nt)
Note: you can use the FT tables.
Answer:
TABLE 3.1
Short Table of Fourier Transforms
g(1)
GF)
g(1)
GỰ)
I u(t)
a >0
10 sin 2nfof
jo.5 [8(f +fo) – 8f – fo)]
a+j2af
2 e u(-t)
a>0
I1 u(t)
1
a - j2nf
2a
3 e-all
a >0
a² + (2xf)²
12 sgn?
4 te-u(t)
a >0
(a +j2nf)?
n!
(4)
17 n
z sinc (æft)
5 re-au(t)
a >0
(a +j2nf)n+
18 2B sinc (27 Bt)
6 8(1)
2B
19 A
Sf)
sinc2
Sf – fo)
20 B sinc? (7Bt)
A
2B
cos 2nfot
0.5 [8(f +fo) + 8(f – fo)]
21 E- 8(t – nT') fo E- 8f – nfo) fo = +
Ln=-00
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