Gujarat Technological UniversitySummer 2024 examination

GTU 3150912 Signals and Systems Summer 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 2:30 PM – 5:00 PM
Questions
5 with internal choice
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Q.1

14 Marks
(a)
3 marks
Explain the Periodic and Non Periodic signal
(b)
4 marks
Explain the classification of signals
(c)
7 marks
Draw below signals: (1) u(−t)u(-t) (2) −4r(t)-4r(t) (3) u(t+4)u(t+4) (4) 4cos⁡(ωt+π/2)4\cos(\omega t + \pi/2)

Q.2

14 Marks
(a)
3 marks
Draw and explain the discrete type of test signals.
(b)
4 marks

If signal cos(13πt)+ 2sin(4πt) is periodic or not? If it is periodic then find its fundamental period.

(c)
7 marks
Define the System and classified it.
(c)
7 marks
Determine whether the system is (i) Linear (ii) causal, (iii) time-invariant (iv) stable: y(n)=n x(n)y(n) = n\,x(n)

Q.3

14 Marks
(a)
3 marks
Explain Aliasing and its effects and how to remove it.
(b)
4 marks
Determine the Nyquist sampling rate and Nyquist sampling interval for x(t)=2 sinc(100πt)x(t) = 2\,\text{sinc}(100\pi t).
(c)
7 marks
Find the convolution of the following sequences:

x(n)=3δ(n+1)−2δ(n)+δ(n−1)+4δ(n−2)x(n) = 3\delta(n+1) - 2\delta(n) + \delta(n-1) + 4\delta(n-2) h(n)=2δ(n−1)+5δ(n−2)+3δ(n−3)h(n) = 2\delta(n-1) + 5\delta(n-2) + 3\delta(n-3)

(a)
3 marks
State and prove Sampling Theorem.
(b)
4 marks
Compute convolution: y(n)=x(n)∗h(n)y(n) = x(n) * h(n), x(n)={1,1,0,1,1}x(n) = \{1, 1, 0, 1, 1\}, 0 is mid point, h(n)={1,−2,−3,4}h(n) = \{1, -2, -3, 4\}, 4 is mid point.
(c)
7 marks
Define convolution and explain the initial value and final value theorem.

Q.4

14 Marks
(a)
3 marks

State and prove Time shifting and Duality properties of continuous time Fourier transform.

(b)
4 marks
Write modulation property of Fourier Transform. Use frequency differentiation property to find the Fourier Transform of x(t)=t e−atu(t)x(t) = t\,e^{-at}u(t).
(c)
7 marks
Give relation between Fourier transform and Laplace transform.
(a)
3 marks
Define Z-transform. Explain region of convergence.
(b)
4 marks
Explain the trigonometric Fourier series.
(c)
7 marks
Find Fourier Series representation for the square wave.

Q.5

14 Marks
(a)
3 marks
Explain Fourier series with any two properties
(b)
4 marks
Find the Z-transform of the unit step signals
(c)
7 marks
Explain the Types of sensors.
(a)
3 marks
Write Differentiation in Z-domain property of z- transform.
(b)
4 marks

Determine the inverse Z-transform of the following X(z)X(z)

X(z)=z2z2−3z+1,∣z∣<12X(z) = \frac{z}{2z^2 - 3z + 1},\quad |z| < \frac{1}{2}

(c)
7 marks
Write a short note on Arduino.

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About this paper

Official Gujarat Technological University (GTU) examination paper for Signals and Systems (Summer 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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