Download GTU BE/B.Tech 2019 Winter 3rd Sem New 3131705 Dynamics Of Linear Systems Question Paper

Download GTU (Gujarat Technological University) BE/BTech (Bachelor of Engineering / Bachelor of Technology) 2019 Winter 3rd Sem New 3131705 Dynamics Of Linear Systems Previous Question Paper

1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3131705 Date: 28/11/2019

Subject Name: Dynamics of Linear Systems
Time: 02:30 PM TO 05:00 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) (i) Define system.
(ii) List out the types of system.
03
(b) Explain convolution property of z-transform. 04
(c) Consider the RC circuit given in the figure below. Assume
that the circuit?s time constant is RC = 1 s. The impulse
response of this circuit is given by h(t) = e
-t
u(t).

Determine the voltage across the capacitor, y(t), resulting
from an input voltage x(t) = u(t) ? u(t-2).


07

Q.2 (a) Use the convolution property to find the FT of the system
output Y(j?) for the following inputs and system impulse
response:
?? ( ?? )= 3?? ??? ?? ( ?? ) ?????? ?( ?? )= 2?? ?2?? ?? ( ?? )
03
(b) Use the convolution property to find the time-domain signal
corresponding to the following frequency-domain
representation:
?? ( ?? ?? ?
)= (
1
1 ? (
1
2
)?? ??? ?
) (
1
1 + (
1
2
)?? ??? ?
)
04
(c) Evaluate the periodic convolution of the sinusoidal signal
?? ( ?? )= 2 cos( 2???? )+ sin ( 4???? )
with the periodic square wave x(t) as shown below:

07
OR
(c) The output of an LTI system in response to an input ?? ( ?? )=
?? ?2?? ?? ( ?? ) is ?? ( ?? )= ?? ??? ?? ( ?? ) . Find the frequency response
and the impulse response of this system.
07
Q.3 (a) Find the DTFT of x[n] = ?? [n] 03
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1
Seat No.: ________ Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY

BE - SEMESTER ? III (New) EXAMINATION ? WINTER 2019
Subject Code: 3131705 Date: 28/11/2019

Subject Name: Dynamics of Linear Systems
Time: 02:30 PM TO 05:00 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) (i) Define system.
(ii) List out the types of system.
03
(b) Explain convolution property of z-transform. 04
(c) Consider the RC circuit given in the figure below. Assume
that the circuit?s time constant is RC = 1 s. The impulse
response of this circuit is given by h(t) = e
-t
u(t).

Determine the voltage across the capacitor, y(t), resulting
from an input voltage x(t) = u(t) ? u(t-2).


07

Q.2 (a) Use the convolution property to find the FT of the system
output Y(j?) for the following inputs and system impulse
response:
?? ( ?? )= 3?? ??? ?? ( ?? ) ?????? ?( ?? )= 2?? ?2?? ?? ( ?? )
03
(b) Use the convolution property to find the time-domain signal
corresponding to the following frequency-domain
representation:
?? ( ?? ?? ?
)= (
1
1 ? (
1
2
)?? ??? ?
) (
1
1 + (
1
2
)?? ??? ?
)
04
(c) Evaluate the periodic convolution of the sinusoidal signal
?? ( ?? )= 2 cos( 2???? )+ sin ( 4???? )
with the periodic square wave x(t) as shown below:

07
OR
(c) The output of an LTI system in response to an input ?? ( ?? )=
?? ?2?? ?? ( ?? ) is ?? ( ?? )= ?? ??? ?? ( ?? ) . Find the frequency response
and the impulse response of this system.
07
Q.3 (a) Find the DTFT of x[n] = ?? [n] 03
2
(b) Determine the Fourier Series coefficients for the signal
defined by
?? ( ?? )= ? ?( t ? 4l)
?
?? = ??

04
(c) Prove the following properties in context of Continuous
Time Fourier Transform:
(i) Time shifting
(ii) Time and frequency scaling
07
OR
Q.3 (a) State Dirichlet condition for Fourier series representation. 03
(b) Prove the duality property of Fourier transform. 04
(c) Determine the appropriate Fourier representations of the
following time domain signals:
(i) x(t) = e
-t
cos(2?t)u(t)
(ii) x(t) = |sin(2?t)|
07
Q.4 (a) Explain the linearity property of Laplace transform. 03
(b) Derive the relationship between Laplace transform and
Fourier transform.
04
(c) Analyze the role of Region of Convergence (ROC) for
defining the stability of system in the context of Laplace
transform.
07
OR
Q.4 (a) Explain the modulation property in context of Fourier
transform.
03
(b) Explain the differencing and summation property of
discrete Fourier transform.
04
(c) Find the inverse Discrete Time Fourier Transform (DTFT)
of
?? ( ?? ?? ?
)=
?
5
6
?? ??? ?
+ 5
1 +
1
6
?? ??? ?
?
1
6
?? ??? ?2

07
Q.5 (a) Explain the linearity property of z-transform. 03
(b) Explain the concept of poles and zeros with respect to z-
transform.
04
(c) Determine the z-transform of the signal
?? [?? ] = ??? [??? ? 1] + (
1
2
)
?? ?? [?? ]
Depict the ROC and the locations of poles and zeros of X(z)
in the z-plane.
07
OR

Q.5 (a) Explain the initial value theorem in conext of z-transform. 03
(b) Determine the z-transform of the signal
?? [?? ] = ?? ?? ?? [?? ]
04
(c) Find the inverse z-transform of
?? ( ?? )=
2 + ?? ?1
1 ?
1
2
?? ?1

with ROC |z| >
1
2

07


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