Download GTU B.Tech 2020 Winter 5th Sem 3150912 Signals And Systems Question Paper

Download GTU (Gujarat Technological University Ahmedabad) B.Tech/BE (Bachelor of Technology/ Bachelor of Engineering) 2020 Winter 5th Sem 3150912 Signals And Systems Previous Question Paper

Seat No.: ________
Enrolment No.___________
GUJARAT TECHNOLOGICAL UNIVERSITY
BE- SEMESTER?V (NEW) EXAMINATION ? WINTER 2020
Subject Code:3150912 Date:01/02/2021
Subject Name:Signals and Systems
Time:10:30 AM TO 12:30 PM Total Marks: 56
Instructions:
1. Attempt any FOUR questions out of EIGHT questions.

2. Make suitable assumptions wherever necessary.

3. Figures to the right indicate full marks.



Marks
Q.1
(a) Compare Analog Signal and Digital Signal
03

(b) Differentiate between continuous and discrete time signal.
04

(c) Explain with Example following properties of system.
07
(1)
Linearity
(2)
Homogeneity
(3)
Additivity
(4) Casuality (5) Shift invariance (6) Stability
(7) Realizability


Q.2
(a) Determine the energy and power of a unit step signal.
03

(b) State and prove the frequency differentiation property of
04
Fourier transform.

(c) Define Laplace transform. Prove linearity property for
07
Laplace transform. State how ROC of Laplace transform is
useful in defining stability of systems.



Q.3
(a) Obtain the DFT of unit impulse (n)
03

(b) Prove the duality or symmetry property of fourier transform.
04

(c) Find the fourier transform of the periodic signal
07
x(t)=cos(20) ()




Q.4
(a) State and prove a condition for a discrete time LTI system to
03
be invertible.

(b) State and prove the time scaling property of Laplace
04
transform.

(c) Find the convolution of two signals X1(t) and X2(t)
07
X`(t)= -4()
X2(t)= ( - 4)



Q.5
(a) State the condition for existence of Fourier integral.
03

(b) Prove that when a periodic signal is time shifted, then the
04
magnitude of its fourier series coefficient remains unchanged.
(|an|=|bn|)

(c) Determine the homogeneous solution of the system described
07
by: () - 3( - 1) - 4( - 2) = ()



Q.6
(a) State and prove the initial value theorem.
03

(b) State and prove the Final value theorem.
04

(c) Explain the trigonometric fourier series with suitable example.
07



Q.7
(a) Explain discrete Fourier transform and enlist its features.
03

(b) Define the region of convergence with respect to z-transform.
04

(c) Define: The Z transform. State and prove Time shifting and
07
Time reversal properties of Z transform



Q.8
(a) Determine the z-transform of following finite duration
03
1

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sequence X(n)={1,2,4,5,0, 7}
(b) Calculate the DFT of the sequence, () = {1,1,0,0}. Verify
04
your answer with IDFT.
(c) Determine if the following systems described by
07
i.
y(t) = sin[x(t+2)];
ii.
y(n)=x[2-n]
are memoryless, causal, linear, time invariant, stable

2

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