Download GTU BE/B.Tech 2019 Winter 4th Sem New 2141005 Signals And Systems Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 4th Sem New 2141005 Signals And Systems Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2141005 Date: 17/12/2019

Subject Name: Signals and Systems

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS

Q.1 (a) Consider an analog pulse
?? (?? ) = {
1 0 ? ?? ? 1
0 ???? ?????????????
Find mathematical expression for ?? (?? )delayed by 2, advanced by 2, and the
reflected signal ?? (??? ).
03
(b) Determine whether or not the following signals is periodic. If a signal is
periodic, determine its fundamental period.
i. ?? (?? ) = cos ?? + ?????? ?2 ??
ii. ?? [?? ] = ?? ?? (
?? 4
)??
04
(c) Evaluate ?? [?? ] = ?? [?? ] ? ?[?? ], by graphical method. where ?? [?? ] and ?[?? ]
are shown figure below.

07

Q.2 (a) Determine the energy and power of a unit step signal. 03
(b) Consider a discrete-time LTI system with impulse response ?[?? ] given by
?[?? ] = ?? ?? ?? [?? ]
i. Is this system causal?
ii. Is this system BIBO stable?

04
(c) Determine natural response of the first order system governed by the
equation,
???? (?? )
???? + 3?? (?? ) = ?? (?? ); ?? (0) = 2
07
OR
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2141005 Date: 17/12/2019

Subject Name: Signals and Systems

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS

Q.1 (a) Consider an analog pulse
?? (?? ) = {
1 0 ? ?? ? 1
0 ???? ?????????????
Find mathematical expression for ?? (?? )delayed by 2, advanced by 2, and the
reflected signal ?? (??? ).
03
(b) Determine whether or not the following signals is periodic. If a signal is
periodic, determine its fundamental period.
i. ?? (?? ) = cos ?? + ?????? ?2 ??
ii. ?? [?? ] = ?? ?? (
?? 4
)??
04
(c) Evaluate ?? [?? ] = ?? [?? ] ? ?[?? ], by graphical method. where ?? [?? ] and ?[?? ]
are shown figure below.

07

Q.2 (a) Determine the energy and power of a unit step signal. 03
(b) Consider a discrete-time LTI system with impulse response ?[?? ] given by
?[?? ] = ?? ?? ?? [?? ]
i. Is this system causal?
ii. Is this system BIBO stable?

04
(c) Determine natural response of the first order system governed by the
equation,
???? (?? )
???? + 3?? (?? ) = ?? (?? ); ?? (0) = 2
07
OR
2
(c) Find the overall impulse response of the system shown in figure below.
Take, ?
1
(?? ) = ???? (?? ); ?
2
(?? ) = 3?? (?? ); ?
3
(?? ) = 2?? (?? );

07
Q.3 (a) Find the Laplace transform of ?? (?? ) = ???? ?? 2
?? . 03
(b) Determine the complex exponential Fourier series representation for the
signals ?? (?? ) = cos (2?? +
?? 4
).
04
(c) Determine the trigonometric Fourier series of periodic impulse train
?? ?? 0
(?? ) = ? ?? (?? ? ?? ?? 0
)
?
?? =??



07
OR
Q.3 (a) State and prove the frequency differentiation property of Fourier transform. 03
(b) Find the Fourier transform of
?? (?? ) = { 2, 1, 2 }.
04
(c) Determine the frequency response of the LTI system defined by,
?? (?? ) = ?? (?? ) + ???? (?? ? 1)
07
Q.4 (a) Determine the z-transform of
?? (?? ) = (?? ? 3)u(n)
03
(b) State and prove shifting property for one sided z-transform. 04
(c) Determine the inverse z-transform of
?? (?? ) =
1
1?0.8?? ?1
+0.12?? ?2
for ROC, |?? | > 0.6.
07
OR
Q.4 (a) Find the even part of signal
?? (?? ) = ?? (?? ) + ?? (??? ).
03
(b) Determine the inverse z-transform of
?? (?? ) = log(1 + ?? ?? ?1
) ; |?? | > |?? |.
04
(c) Determine the impulse response h(n) for the system described by the second
order difference equation,
?? (?? ) ? 4?? (?? ? 1) + 4?? (?? ? 2) = ?? (?? ? 1)
07
Q.5 (a) Test the following systems for linearity.
?? (?? ) = 4?? (?? ) + 2
???? (?? )
????
.
03
(b) State and prove the time scaling property of Laplace transform. 04
(c) A system has impulse response h(n) given by, 07
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? IV (New) EXAMINATION ? WINTER 2019
Subject Code: 2141005 Date: 17/12/2019

Subject Name: Signals and Systems

Time: 10:30 AM TO 01:00 PM Total Marks: 70

Instructions:

1. Attempt all questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.


MARKS

Q.1 (a) Consider an analog pulse
?? (?? ) = {
1 0 ? ?? ? 1
0 ???? ?????????????
Find mathematical expression for ?? (?? )delayed by 2, advanced by 2, and the
reflected signal ?? (??? ).
03
(b) Determine whether or not the following signals is periodic. If a signal is
periodic, determine its fundamental period.
i. ?? (?? ) = cos ?? + ?????? ?2 ??
ii. ?? [?? ] = ?? ?? (
?? 4
)??
04
(c) Evaluate ?? [?? ] = ?? [?? ] ? ?[?? ], by graphical method. where ?? [?? ] and ?[?? ]
are shown figure below.

07

Q.2 (a) Determine the energy and power of a unit step signal. 03
(b) Consider a discrete-time LTI system with impulse response ?[?? ] given by
?[?? ] = ?? ?? ?? [?? ]
i. Is this system causal?
ii. Is this system BIBO stable?

04
(c) Determine natural response of the first order system governed by the
equation,
???? (?? )
???? + 3?? (?? ) = ?? (?? ); ?? (0) = 2
07
OR
2
(c) Find the overall impulse response of the system shown in figure below.
Take, ?
1
(?? ) = ???? (?? ); ?
2
(?? ) = 3?? (?? ); ?
3
(?? ) = 2?? (?? );

07
Q.3 (a) Find the Laplace transform of ?? (?? ) = ???? ?? 2
?? . 03
(b) Determine the complex exponential Fourier series representation for the
signals ?? (?? ) = cos (2?? +
?? 4
).
04
(c) Determine the trigonometric Fourier series of periodic impulse train
?? ?? 0
(?? ) = ? ?? (?? ? ?? ?? 0
)
?
?? =??



07
OR
Q.3 (a) State and prove the frequency differentiation property of Fourier transform. 03
(b) Find the Fourier transform of
?? (?? ) = { 2, 1, 2 }.
04
(c) Determine the frequency response of the LTI system defined by,
?? (?? ) = ?? (?? ) + ???? (?? ? 1)
07
Q.4 (a) Determine the z-transform of
?? (?? ) = (?? ? 3)u(n)
03
(b) State and prove shifting property for one sided z-transform. 04
(c) Determine the inverse z-transform of
?? (?? ) =
1
1?0.8?? ?1
+0.12?? ?2
for ROC, |?? | > 0.6.
07
OR
Q.4 (a) Find the even part of signal
?? (?? ) = ?? (?? ) + ?? (??? ).
03
(b) Determine the inverse z-transform of
?? (?? ) = log(1 + ?? ?? ?1
) ; |?? | > |?? |.
04
(c) Determine the impulse response h(n) for the system described by the second
order difference equation,
?? (?? ) ? 4?? (?? ? 1) + 4?? (?? ? 2) = ?? (?? ? 1)
07
Q.5 (a) Test the following systems for linearity.
?? (?? ) = 4?? (?? ) + 2
???? (?? )
????
.
03
(b) State and prove the time scaling property of Laplace transform. 04
(c) A system has impulse response h(n) given by, 07
3
?(?? ) = ?0.25?? (?? + 1) + 0.5?? (?? ) ? 0.25?? (?? ? 1).
i. Is the system BIBO stable?
ii. Is the system causal? Justify your answer.
OR
Q.5 (a) i. Define Fourier transform.
ii. State the condition for existence of Fourier integral.
03
(b) Calculate the DFT of the sequence,
?? (?? ) = {1,1, ?2, ?2}
04
(c) Define ROC for z-transform. List the property of ROC. 07

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