Gujarat Technological UniversitySummer 2026 examination

GTU BE03000171 Signals and Systems Summer 2026 Question Paper & PDF

B.E. · EC Engineering · Semester 3 · Subject code BE03000171
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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
Find even and odd part of x(t)=u(−t)x(t) = u(-t).
(b)
4 marks
Obtain relationship between Laplace and Fourier Transform.
(c)
7 marks
Write the properties of ROC of Z-Transform.

Q.2

14 Marks
(a)
3 marks
Define periodic and aperiodic signal. Also check whether sin⁡(5πt)\sin(5\pi t) is periodic or not.
(b)
4 marks
Compare Energy and Power signals with example.
(c)
7 marks
Explain Aliasing and its effects.
(c)
7 marks
Explain in detail Sampling Theorem.

Q.3

14 Marks
(a)
3 marks
Prove Associative property of Convolution sum.
(b)
4 marks

Determine whether the following system with impulse response h(t)=e−5tu(t)h(t) = e^{-5t}u(t) is stable or not.

(c)
7 marks
Derive Fourier co-efficients of the Trigonometric Fourier series of an even symmetry periodic signal.
(a)
3 marks
Prove Commutative property of convolution sum.
(b)
4 marks
State and prove time differentiation property of Z-Transform.
(c)
7 marks
Compute y(t)=x(t)∗h(t)y(t) = x(t)*h(t) if x(t)=u(t)x(t) = u(t) and h(t)=u(t+3)h(t) = u(t+3).

Q.4

14 Marks
(a)
3 marks
Obtain Z-Transform of unit step signal.
(b)
4 marks
State and prove time scaling and time shifting property of Fourier transform
(c)
7 marks
Obtain linear convolution of two discrete time signals given as :

x[n]=u[n]x[n] = u[n] and h[n]=anu[n],a<1h[n] = a^n u[n], a < 1.

(a)
3 marks
Obtain Fourier Transform of unit step signal.
(b)
4 marks
Prove the duality theorem of Fourier Transform.
(c)
7 marks
Determine z Transform of following sequences. Also draw the ROC:
1x[n]=u(n+2)x[n] = u(n+2)
2x[n]=4nu[n]+5nu[−n−1]x[n] = 4^n u[n] + 5^n u[-n - 1]

Q.5

14 Marks
(a)
3 marks
Compute DFT of the sequence x[n]={2,0,3,1}x[n] = \{2,0,3,1\}
(b)
4 marks
State & prove a condition for a discrete time LTI system to be stable.
(c)
7 marks
Determine the following system described by y(t)=cos⁡[x(t−2)]y(t)= \cos[x(t-2)] is memory less, causal, linear, time-invariance or stable?
(a)
3 marks
Compute DFT of the sequence x[n]={−2,3,−3,−1}x[n] = \{-2,3,-3,-1\}
(b)
4 marks
Prove that DT LTI system is causal if and only if h(n)=0h(n) = 0 for n<0n < 0.
(c)
7 marks

Explain following property for the system y(t)=3x(−t)−14y(t) = 3x(-t) - 14.

iLinearity (ii) Time-invariance (iii) Causality (iv) Dynamicity

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About this paper

Official Gujarat Technological University (GTU) examination paper for Signals and Systems (Summer 2026, B.E. · EC Engineering, Sem 3). 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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