Download GTU B.Tech 2020 Summer 4th Sem 2141005 Signals And Systems Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Summer 4th Sem 2141005 Signals And Systems Previous Question Paper

Seat No.: ________
Enrolment No.___________


GUJARAT TECHNOLOGICAL UNIVERSITY
BE - SEMESTER? IV EXAMINATION ? SUMMER 2020
Subject Code: 2141005 Date:02/11/2020
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) Based upon nature and characteristics in the time domain,
03
classify signals broadly. In each of the broad domains enlist
signals further classification.

(b) Sketch each of the following signals.
04
(i)
x[n] = u[n] - u[n - 5]
(ii)
x(t) = u(t+4) . u(-t +4)

(c) Classify following systems as : Causal or non-causal; Linear
07
or nonlinear and Time invariant or time variant
y(n) = log10 x(n)
y(n)= n x(n) + x(n+2)


Q.2 (a) State and prove Linearity property of LTI systems using Laplace
03
transform.

(b) For LTI system, if input sequence is x(n) and impulse response
04
is defined as h(n), derive equation for discrete time convolution
sum y(n).

(c) Consider a causal LTI system with impulse response
07
(
h t)
4
e tu(t). Find the output of the system for an input
t
x t
( ) e
.
3


OR


(c)
Solve the following difference equation
07
y(n) 2 y(n )
1 x(n)
1
With x( )
n
( )n
u( )
n and initial condition y(-1)=1
3
Q.3 (a) Enlist dirichelts conditions for existence of Fourier transform.
03

(b) Find discrete time linear convolution of following two sequences
04
using matrices method.
x(n) 2 (n )
1 3 (n) (n )
1 2 (n )
2
h(n) 2 (n )
1 3 (n )
2 4 (n )
3

(c) Compute the Fourier transform for the signal x(t) in following
07
Figure:01
1

---

Figure:01


OR

Q.3 (a) Explain distributive property of LTI systems with suitable
03
figures.

(b) An LTI system has impulse response given by h(n)={2,1,2,1} .
04
Find its response to input x(n)= {1,-2,4}.

(c) Compute the Fourier transform for the signal x(t) in following
07
Figure: 02.
Figure:02
Q.4 (a) Prove that for causal sequences, the ROC of Z transform is
03
exterior of a circle.

(b) Find the Fourier transform of cosine wave cos w t . Draw its
04
0
magnitude spectrum.

(c) State and prove (a) Differentiation in time domain and (b) time
07
shifting properties of LTI systems using Fourier transform.

OR

Q.4 (a) Explain with suitable mathematical equations, relation between
03
Laplace Transform and Fourier Transform,

(b) Using properties of Z transform, compute Z transform for
04
following signals.
x(n)= u(-n)
x(n)= u(-n-2)

(c) Find
fourier transforms of unit impluse function. Define clearly
07
Signam function (sgn(t)) and with its help find FT of unit step
function.
Q.5 (a) Find inverse Z transform of
03
1
z
X (z)
; RoC z 1
3 4 1
2
z z

(b) Using Z transform, find the convolution of the sequences
04
x ( )
n
};
4
,
3
,
2
,
1
{
x ( )
n
}
1
,
1
,
1
{
1
2

(c) Determine steady state (forced) response for the system with
07
1
impulse
response
(
h )
n
( )n
u( )
n
for
the
input
2
x(n) [cos( n
)]u(n) .


OR
Q.5 (a) Find inverse Z transform of
03
2

---

3
2
1
2
3
X (z) 2z z z 3 2z 4
z z
(b) Write the properties of ROC of X(z).

04

(c) An LTI system is described by the difference equation
07
9
1
y( )
n y(n )
1 y(n )
2 x( )
n 3x(n )
1
4
2
Specify the ROC of H(z) and determine h(n) for the following
conditions,
(i)
The system is stable
(ii)
The system is causal
3

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