Gujarat Technological UniversityWinter 2024 examination

GTU 3150912 Signals and Systems Winter 2024 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 10:30 AM – 1:00 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Check linearity of a system described by y[n]=x[n]+12x[n−2]y[n] = x[n] + \dfrac{1}{2x[n-2]}
(b)
4 marks
Prove commutative, distributive and associative properties of convolution integral
(c)
7 marks
Convolve x[n]={−1,4,3↑,2,−2}x[n] = \{-1, 4, \underset{\uparrow}{3}, 2, -2\} and h[n]={1,2↑,−1,1}h[n] = \{1, \underset{\uparrow}{2}, -1, 1\} (the arrow marks n=0n = 0)

Q.2

14 Marks
(a)
3 marks
Define (i) Periodicity of a signal (ii) Non-causal signals (iii) Even signal and give example of each
(b)
4 marks
Check stability of a system described by y[n]=x[n]+12x[n−1]+14x[n−2]y[n] = x[n] + \dfrac{1}{2}x[n-1] + \dfrac{1}{4}x[n-2]
(c)
7 marks
Given impulse response of the system h(t)=e−2tu(t)h(t) = e^{-2t}u(t). Obtain the output of the system for x(t)=e−4t[u(t)−u(t−2)]x(t) = e^{-4t}[u(t) - u(t-2)]
(c)
7 marks
Given impulse response of the system h(t)=u(t−3)h(t) = u(t-3). Obtain the output of the system for x(t)=u(t+2)x(t) = u(t+2)

Q.3

14 Marks
(a)
3 marks
Check causality of a system described by y(t)=∫−∞3tx(τ) dτy(t) = \int_{-\infty}^{3t} x(\tau)\,d\tau
(b)
4 marks
State and prove linearity and convolution property of z- transform
(c)
7 marks
Find Fourier transform of x[n]=2nsin⁡[(π/4)n] u[−n]x[n] = 2^n \sin[(\pi/4)n]\,u[-n]
(a)
3 marks
State Dirichlet conditions for existence of Fourier transform
(b)
4 marks
Obtain the energy of the signal x(t)x(t) shown below
GTU Signals and Systems (3150912) Winter 2024 Question 3 OR (b) Diagram
(c)
7 marks
Obtain Fourier transform of (a) x(t)=e−2(t−1)u(t−1)x(t) = e^{-2(t-1)}u(t-1) (b) x(t)=δ(t+2)+δ(t−2)x(t) = \delta(t+2) + \delta(t-2)

Q.4

14 Marks
(a)
3 marks
Prove the nonexistence of Fourier series co-efficients a0a_0 and ana_n for a periodic waveform with odd symmetry
(b)
4 marks
Obtain Laplace transform of x(t)=e−atu(t)x(t) = e^{-at}u(t) by direct integration.
(c)
7 marks

Explain zero order hold with its mathematical representation. Write at least three advantages and disadvantages of zero order hold

(a)
3 marks
Compare Fourier series and Fourier transform
(b)
4 marks
Obtain Laplace transform of x(t)=(e2t−2e−t) u(t)x(t) = (e^{2t} - 2e^{-t})\,u(t)
(c)
7 marks
Explain aliasing by taking a suitable example

Q.5

14 Marks
(a)
3 marks
Explain signal reconstruction from its sampled form
(b)
4 marks
State and prove the final value theorem
(c)
7 marks
List at least four types of actuators used with Arduino with their application
(a)
3 marks
State and explain sampling theorem
(b)
4 marks
State the properties of ROC of z-transform
(c)
7 marks
List at least seven types of sensors used with Arduino with their application in brief

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About this paper

Official Gujarat Technological University (GTU) examination paper for Signals and Systems (Winter 2024, 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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