# Download GTU B.Tech 2020 Summer 3rd Sem 3131705 Dynamics Of Linear Systems Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 3rd Sem 3131705 Dynamics Of Linear Systems Previous Question Paper

Seat No.: ________
Enrolment No.___________

GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER? III EXAMINATION ? SUMMER 2020
Subject Code: 3131705 Date:27/10/2020
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) Explain continuous-time and discrete-time signals with
03
suitable example.

(b) For each of the following input-output relationships,
04
determine whether the corresponding system is linear, time
invariant or both.
1. y(t) = t2 x(t- 1)
2. y[n] = x[n + 1] - x[n- 1]

(c) What is time-variant and time-invariant system? Determine
07
causality and stability of the following discrete-time systems
with justification. Consider y[n] is the system output and x[n]
is the system input.
1. y[n] = x[- n]
2. y[n] = x[n - 2] - 2x[n - 8]

Q.2 (a) Explain LTI systems with and without memory.
03

(b) A linear time-invariant system is characterized by its impulse
04
1 n
response h[ n ] = u(n).
2
Determine energy density spectrum of the output signal when the
1 n
[
x n] u(n).
system is excited by the signal
4

(c) Compute and plot the convolution y[ n ] = x[ n ] * h[ n ], where
07
n
1
x[ n ] = and h[ n ] = u[ n - 1].
3

OR

(c) Explain commutative and distributive property of a LTI
07
system.
Q.3 (a)
03
For x(t) 1 sin w t 2cos w t co
w t
0
0
s 2
0
4 .
Determine Fou rier series coefficient using complex exponential
representation.

(b) Discuss applications of frequency-selective filters.
04

(c) Discuss the properties of continuous-time Fourier series.
07

1

OR
Q.3 (a) Each of the two sequences x [ ]
n and x [ ]
n has a period N =
03
1
2
4, and the corresponding Fourier series coefficients are
specified as x [n]
a and x [n]
b
1
k
2
k
Where,
1
1
a = a = a = a =1 and b = b = b =b =1. Using the
0
3
1
2
2
2
0
1
2
3
multiplication property, determine the Fourier series coefficients
c for the signal g[n] = x [ ]
n x [ ]
n .
k
1
2

(b) Discuss applications of frequency-shaping filters.
04

Determine whether each of the following statements is true or
07
1. An odd and imaginary signal always has an odd and
imaginary Fourier transform.
2. The convolution of an odd Fourier transform with an
even Fourier transform is always odd.
Q.4 (a) Explain time reversal and linearity property for the discrete
03
time Fourier transforms.

(b) Determine the Fourier transform for w< for the
04
periodic signal x(n) sin n
3
4 .

(c) Consider a discrete-time LTI system with impulse response
07
1 n
h(n) u(n).
2
Use Fourier transforms to determine the response for the input
3 n
x(n) u(n).
4

OR

Q.4 (a) Explain differentiation and integration property for the
03
continuous time Fourier transforms.

(b) Determine the Fourier transform of periodic signal
04
x(t) 1 co
s 6t
8 .

(c) Compute the Fourier transform of each of the following
07
signals:
1. [
x n] [
u n 2] [
u n 6]
1 n
2. [
x n]
[
u n ]
1
2
Q.5 (a) Determine the Laplace transform and the associated region of
03
convergence for (
x t)
2
e tu(t)
3
e tu(t).

(b) Determine the function of time x(t), for the following Laplace
04
transforms and their associated regions of convergence:
1
,
{
e }
s >0.
2
s 9

(c) Explain properties of the Z-transform.
07

2

OR
Q.5 (a) Find Z-transform and region of convergence of
03
1 n
1 n
x(n) 7 u(n) 6 u(n).
3
2
(b) Find inverse Z-transform for X (z) log 1
(
1
az ) , z > a .
04
(c) Consider the system function corresponding to causal LTI
07
1
systems: H(z)=
.
1
1 2
2 1 1
1
( z z
1
)(
2
z z )
4
3
9
1. Draw a direct-form block diagram.
2. Draw a block diagram that corresponds to the cascade
connection of two second-order block diagrams. Each
second-order block diagram should be in direct form.

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