Signals And Systems 2nd Edition Textbook Solutions 1a64b
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Chapter 3, Problem 22P
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Signals and Systems (2nd Edition)
Problem
Determine the Fourier series representations for the following signals: (a) Each x(t) illustrated in Figure P3.22(a)--(f). (b) x(t) periodic with period 2 and
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
Chapter 1 Chapter 2 Chapter 3 1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P
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19P
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20P 21P
Chapter 3, Problem 22P
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22P 23P 24P 25P 26P 27P 28P 29P 30P 31P 32P 33P 34P
Step-by-step solution
35P
Step 1 of 24
36P 37P
(a) (a) Consider the following waveform: 38P 39P 40AP 41AP 42AP 43AP 44AP 45AP
Figure 1
46AP 47AP
Comment
48AP
Step 2 of 24
49AP 50AP 51AP
Determine the Fourier series representation for the signal in Figure 1. Clearly, from the waveform in Figure 1:
52AP 53AP
Calculate the dc component of
54AP
The fundamental period,
55AP
Calculate
56AP
.
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57AP
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58AP 59AP
Chapter 3, Problem 22P
60AP 61AP 62AP
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ON
Since, the waveform in Figure 1 is symmetrical about t-axis (X-axis), therefore, the dc component of
is:
Determine the Fourier series coefficients of
63AP 64AP 65EP 66EP 67EP 68EP 69EP
Comment 70EP 71EP
Step 3 of 24
Chapter 4 Chapter 5
Show all steps:
Simplify further.
Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11
Hence, the Fourier series representation of
Thus, the Fourier series representation of
is:
is
.
Comment
Step 4 of 24 (a) (b) Consider the following waveform:
TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Figure 2
Comment
Step 5 of 24 Determine the Fourier series representation for the signal in Figure 2. Clearly, from the waveform in Figure 2: The fundamental period, Calculate
For interval
,
is defined as:
Calculate the dc component of
Simplify further.
Comment
.
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Step 6 of 24 EXPERT Q&A
Determine the Fourier series coefficients of
Chapter 3, Problem 22P
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Simplify further.
Comment
Step 7 of 24 Simplify further.
Simplify further.
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Comment
Step 8 of 24 Since,
Hence,
Thus, the Fourier series representation of
is
Comment
Step 9 of 24 (a) (c) Consider the following waveform:
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Chapter 3, Problem 22P
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Figure 3
Comment
Step 10 of 24
Determine the Fourier series representation for the signal in Figure 3. Clearly, from the waveform in Figure 3: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
.
Simplify further.
Hence, the dc component of
is:
Comment
Step 11 of 24
Determine the Fourier series coefficients of
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Simplify further.
TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Comment
Step 12 of 24 Simplify further.
Thus, for
Comment
Step 13 of 24 (a) (d) Consider the following waveform:
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Chapter 3, Problem 22P
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Figure 4
Comment
Step 14 of 24 Determine the Fourier series representation for the signal in Figure 4. Clearly, from the waveform in Figure 4: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
Hence, the dc component of
.
is:
Determine the Fourier series coefficients of
Where,
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Chapter 3, Problem 22P
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Hence,
Thus, for
Comment
Step 15 of 24 (a) (e) Consider the following waveform:
Figure 5
Comment
Step 16 of 24 Determine the Fourier series representation for the signal in Figure 5. Clearly, from the waveform in Figure 5: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
.
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Hence, the dc component of
is:
Comment
Step 17 of 24
Determine the Fourier series coefficients of
Simplify further.
Thus,
.
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TEXTBOOK SOLUTIONS Comment
Chapter 3, Problem 22P
Step 18 of 24
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(a) (f) Consider the following waveform:
Figure 6
Comment
Step 19 of 24
Determine the Fourier series representation for the signal in Figure 6. Clearly, from the waveform in Figure 6: The fundamental period, For interval
,
The fundamental period of
Hence, the dc component of
is defined as:
is
is:
Comment
Step 20 of 24
Determine the Fourier series coefficients of
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Chapter 3, Problem 22P
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Simplify further.
Simplify further.
Thus, .
Comment
Step 21 of 24
(b) Consider the following signal: for The period of
is:
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Determine the Fourier series coefficients of TEXTBOOK SOLUTIONS EXPERT Q&A
Chapter 3, Problem 22P
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Simplify further.
Thus, .
Comment
Step 22 of 24 (c) Consider the following signal:
The period of
is:
Calculate the dc component of the signal.
Simplify further.
Hence, the dc component of
is:
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TEXTBOOK SOLUTIONS Comment
Chapter 3, Problem 22P
Step 23 of 24
Determine the Fourier series coefficients of
Simplify further.
Comment
Step 24 of 24 Simplify further.
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Chapter 3, Problem 22P
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Show all steps:
Simplify further.
Thus, .
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TEXTBOOK SOLUTIONS
home / study / engineering / electrical engineering / signal theory / solutions manual / signals and systems / 2nd edition
Chapter 3, Problem 22P
Bookmark
Signals and Systems (2nd Edition)
Problem
Determine the Fourier series representations for the following signals: (a) Each x(t) illustrated in Figure P3.22(a)--(f). (b) x(t) periodic with period 2 and
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EXPERT Q&A
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
Chapter 1 Chapter 2 Chapter 3 1P 2P 3P 4P 5P 6P 7P 8P 9P 10P 11P 12P 13P 14P 15P 16P 17P 18P
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19P
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20P 21P
Chapter 3, Problem 22P
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22P 23P 24P 25P 26P 27P 28P 29P 30P 31P 32P 33P 34P
Step-by-step solution
35P
Step 1 of 24
36P 37P
(a) (a) Consider the following waveform: 38P 39P 40AP 41AP 42AP 43AP 44AP 45AP
Figure 1
46AP 47AP
Comment
48AP
Step 2 of 24
49AP 50AP 51AP
Determine the Fourier series representation for the signal in Figure 1. Clearly, from the waveform in Figure 1:
52AP 53AP
Calculate the dc component of
54AP
The fundamental period,
55AP
Calculate
56AP
.
Show all steps:
ON
57AP
TEXTBOOK SOLUTIONS
Search
EXPERT Q&A
58AP 59AP
Chapter 3, Problem 22P
60AP 61AP 62AP
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ON
Since, the waveform in Figure 1 is symmetrical about t-axis (X-axis), therefore, the dc component of
is:
Determine the Fourier series coefficients of
63AP 64AP 65EP 66EP 67EP 68EP 69EP
Comment 70EP 71EP
Step 3 of 24
Chapter 4 Chapter 5
Show all steps:
Simplify further.
Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10 Chapter 11
Hence, the Fourier series representation of
Thus, the Fourier series representation of
is:
is
.
Comment
Step 4 of 24 (a) (b) Consider the following waveform:
TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Figure 2
Comment
Step 5 of 24 Determine the Fourier series representation for the signal in Figure 2. Clearly, from the waveform in Figure 2: The fundamental period, Calculate
For interval
,
is defined as:
Calculate the dc component of
Simplify further.
Comment
.
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TEXTBOOK SOLUTIONS
Step 6 of 24 EXPERT Q&A
Determine the Fourier series coefficients of
Chapter 3, Problem 22P
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Simplify further.
Comment
Step 7 of 24 Simplify further.
Simplify further.
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Comment
Step 8 of 24 Since,
Hence,
Thus, the Fourier series representation of
is
Comment
Step 9 of 24 (a) (c) Consider the following waveform:
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Chapter 3, Problem 22P
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Figure 3
Comment
Step 10 of 24
Determine the Fourier series representation for the signal in Figure 3. Clearly, from the waveform in Figure 3: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
.
Simplify further.
Hence, the dc component of
is:
Comment
Step 11 of 24
Determine the Fourier series coefficients of
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Simplify further.
TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Comment
Step 12 of 24 Simplify further.
Thus, for
Comment
Step 13 of 24 (a) (d) Consider the following waveform:
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Figure 4
Comment
Step 14 of 24 Determine the Fourier series representation for the signal in Figure 4. Clearly, from the waveform in Figure 4: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
Hence, the dc component of
.
is:
Determine the Fourier series coefficients of
Where,
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ON
TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Hence,
Thus, for
Comment
Step 15 of 24 (a) (e) Consider the following waveform:
Figure 5
Comment
Step 16 of 24 Determine the Fourier series representation for the signal in Figure 5. Clearly, from the waveform in Figure 5: The fundamental period, For interval
,
is defined as:
Calculate the dc component of
.
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Show all steps:
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Hence, the dc component of
is:
Comment
Step 17 of 24
Determine the Fourier series coefficients of
Simplify further.
Thus,
.
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TEXTBOOK SOLUTIONS Comment
Chapter 3, Problem 22P
Step 18 of 24
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(a) (f) Consider the following waveform:
Figure 6
Comment
Step 19 of 24
Determine the Fourier series representation for the signal in Figure 6. Clearly, from the waveform in Figure 6: The fundamental period, For interval
,
The fundamental period of
Hence, the dc component of
is defined as:
is
is:
Comment
Step 20 of 24
Determine the Fourier series coefficients of
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Simplify further.
Simplify further.
Thus, .
Comment
Step 21 of 24
(b) Consider the following signal: for The period of
is:
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Determine the Fourier series coefficients of TEXTBOOK SOLUTIONS EXPERT Q&A
Chapter 3, Problem 22P
Bookmark
Simplify further.
Thus, .
Comment
Step 22 of 24 (c) Consider the following signal:
The period of
is:
Calculate the dc component of the signal.
Simplify further.
Hence, the dc component of
is:
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Show all steps:
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TEXTBOOK SOLUTIONS Comment
Chapter 3, Problem 22P
Step 23 of 24
Determine the Fourier series coefficients of
Simplify further.
Comment
Step 24 of 24 Simplify further.
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Show all steps:
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TEXTBOOK SOLUTIONS
Chapter 3, Problem 22P
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Show all steps:
Simplify further.
Thus, .
Comment
Was this solution helpful?
33
2
Electrical Engineering Chegg tutors who can help right now José Á.
Universidad Central de…
Nishit G. BITS Pilani
Mohit M.
BITS Pilani Goa Campus
Jay N.
Columbia University
Pathanjali D.
BITS Pilani Goa Campus
Search
EXPERT Q&A
90
18
5
21
51
ON
ME A TUTOR TEXTBOOK SOLUTIONS FIND EXPERT Q&A
Chapter 3, Problem 22P
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