Gujarat Technological UniversitySummer 2023 examination

GTU 3150912 Signals and Systems Summer 2023 Question Paper & PDF

B.E. · Electrical Engineering · Semester 5 · Subject code 3150912
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Total
70 marks
To pass
23 marks (33%)
Duration
2.5 Hours 2:30 PM – 5:00 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Explain with Example following properties of system.
1Linearity
2Homogeneity
3Shift invariance
(b)
4 marks
Define energy for continuous-time and discrete-time signals.
(c)
7 marks

Write the properties of convolution and explain them with suitable example.

Q.2

14 Marks
(a)
3 marks

Give expression of trigonometric Fourier Series. Define coefficients of DC, fundamental and harmonics.

(b)
4 marks

State and prove a condition for a discrete time LTI system to be invertible.

(c)
7 marks

Perform Linear convolution of following (the arrow marks n=0n = 0):

1x(n)={1,1,0↑,1,1}x(n) = \{1, 1, \underset{\uparrow}{0}, 1, 1\} & h(n)={1,−2,−3,4↑}h(n) = \{1, -2, -3, \underset{\uparrow}{4}\}
2x(n)={1,2,3,1}x(n) = \{1, 2, 3, 1\} & h(n)={1,2↑,1,−1}h(n) = \{1, \underset{\uparrow}{2}, 1, -1\}
3x(n)={1,2↑,1,−1}x(n) = \{1, \underset{\uparrow}{2}, 1, -1\} & h(n)={1,2↑,−3,4}h(n) = \{1, \underset{\uparrow}{2}, -3, 4\}
(c)
7 marks

An LTI system is described by the difference equation

y(n)=x(n)+0.81x(n−1)−0.81x(n−2)−0.45y(n−2)y(n) = x(n) + 0.81x(n-1) - 0.81x(n-2) - 0.45y(n-2)
Determine transfer function of the system. Draw pole zero plot and assess stability.

Q.3

14 Marks
(a)
3 marks
Define Fourier transform for continuous-time signal.
(b)
4 marks
Find the Fourier transform of cosine wave cos⁡ω0t\cos \omega_0 t. Draw its magnitude spectrum.
(c)
7 marks
State and explain each properties of ROC of z-transform.
(a)
3 marks
Give relationship between Laplace transform and Fourier transform.
(b)
4 marks

Using properties of Z transform, compute Z transform for following signals.

1x(n)= u(-n),
2x(n)= u(-n-2)
(c)
7 marks

State and prove time shifting and time-differentiation properties of Laplace transform.

Q.4

14 Marks
(a)
3 marks

Define the terms

1Zero-order hold
2First-order hold
3Ideal interpolation.
(b)
4 marks
Distinguish continuous time systems and discrete time systems
(c)
7 marks

Explain the any application of modulation for communication in signal and system.

(a)
3 marks
What is Aliasing?
(b)
4 marks
What are the effects of under sampling of a signal?
(c)
7 marks
Explain in detail of mathematical model for reconstruction.

Q.5

14 Marks
(a)
3 marks

What is IOT? Draw the block diagram of any application of an IOT based system.

(b)
4 marks

Explain with diagram any four sensors which used in IOT application

(c)
7 marks

Explain with circuit diagram of any application based on Arduino with sensor & actuators.

(a)
3 marks
Explain Input and output pins of Arduino.
(b)
4 marks
Explain the different types of Actuators.
(c)
7 marks

Explain with the circuit diagram of temperature measurement 0 to 100 ºC using LM35 with 16x2 LCD display using Arduino. Also write the program.

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About this paper

Official Gujarat Technological University (GTU) examination paper for Signals and Systems (Summer 2023, B.E. · Electrical Engineering, Sem 5). Features complete 70-mark regular & remedial examination pattern, official marking distribution across all 5 questions, and direct 1-click official PDF download.

Transcribed for student exam preparation from Gujarat Technological University official examination archives. Questions, syllabus guidelines, and curriculum marking schemes remain the intellectual property of Gujarat Technological University.

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