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Gujarat Technological University

This document is an exam for a Signals and Systems course, containing 5 questions testing various concepts: 1. Question 1 covers Fourier series, asking about trigonometric Fourier series expressions, periodicity testing, and complex exponential Fourier series. 2. Question 2 covers even/odd parts of signals, energy signals, and testing if systems are linear/time-invariant/causal/stable. 3. Question 3 covers convolution, either convolution sums/properties or Fourier transform properties and using convolution/inverse Fourier transform. 4. Question 4 covers Z-transforms, either properties of the region of convergence, time shifting properties, or using Z-transforms to solve a difference equation. 5.

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132 views2 pages

Gujarat Technological University

This document is an exam for a Signals and Systems course, containing 5 questions testing various concepts: 1. Question 1 covers Fourier series, asking about trigonometric Fourier series expressions, periodicity testing, and complex exponential Fourier series. 2. Question 2 covers even/odd parts of signals, energy signals, and testing if systems are linear/time-invariant/causal/stable. 3. Question 3 covers convolution, either convolution sums/properties or Fourier transform properties and using convolution/inverse Fourier transform. 4. Question 4 covers Z-transforms, either properties of the region of convergence, time shifting properties, or using Z-transforms to solve a difference equation. 5.

Uploaded by

vanditasathwara
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Seat No.: ________ Enrolment No.

___________

GUJARAT TECHNOLOGICAL UNIVERSITY


BE - SEMESTER–V (NEW) EXAMINATION – WINTER 2021
Subject Code:3150912 Date:27/12/2021
Subject Name:Signals and Systems
Time:02:30 PM TO 05:00 PM Total Marks: 70
Instructions:
1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Simple and non-programmable scientific calculators are allowed.

MARKS
Q.1 (a) Give expression of trigonometric Fourier Series. Define coefficients of 03
DC, fundamental and harmonics.
(b) Check whether the signal x(t)=2cos(100πt)+5sin(50t) is periodic or not. 04

(c) Obtain complex exponential Fourier series for sin ωt and cos ωt. Assume 07
ω to be constant.

Q.2 (a) Find even part of signal x(n)=u(n)-u(n-4). 03


(b) Define energy signal. Find the energy of the signal x(t)=5e-4tu(t) 04
(c) Check whether the system described by the equation y(t)=10x(t)+5 is 07
linear, static, time invariant, causal and stable.
OR
(c) Check whether the system described by the equation y(n)=x(n)u(n) is 07
linear, static, time invariant, causal and stable.
Q.3 (a) Give the convolution sum and integral formulas. 03
(b) List and prove any two properties of convolution sum. 04
(c) Convolve x(t)=e-3t [u(t)-u(t-2)] and h(t)=e-t u(t). 07
OR
Q.3 (a) State the linearity and time shifting property of Fourier transform. 03
(b) Prove convolution property of Fourier transform. 04
(c) Find inverse Fourier transform of 07
2jω
X(ω)= ----------
(2+jω)2
Q.4 (a) Define Z-transform. What is ROC? 03
(b) Find the Z-transform of 4nu(n). 04
(c) Find inverse Z-transform of 07
(z+4)
X(z) = ------------------
( z2-4z+3 )
Assume right-sided sequence.
OR
Q.4 (a) State any three properties of ROC of Z-transform. 03
(b) State and prove the time shifting property of the 04
Z-transform.
(c) Solve the difference equation y(n)-0.5y(n-1) = δ(n) using Z-transform. 07

Q.5 (a) What is zero-order hold in sampling? 03


1
(b) What are the effects of under sampling of a signal ? 04
(c) Describe various types of sensors used for IoT applications. 07
OR
Q.5 (a) Explain the reconstruction of a signal from its samples. 03
(b) Explain any one practical application of Signals and Systems theory. 04
(c) Explain working of any system based on Arduino. 07

*************

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