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Gujarat Technological University

This document outlines the examination details for the Signal & Systems subject at Gujarat Technological University for the Winter 2023 semester. It includes instructions for the exam, a breakdown of questions with marks allocation, and various topics such as convolution, Fourier transforms, and system properties. The exam is scheduled for January 17, 2024, and consists of multiple questions requiring theoretical explanations and calculations.

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krishbhavsar69
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28 views2 pages

Gujarat Technological University

This document outlines the examination details for the Signal & Systems subject at Gujarat Technological University for the Winter 2023 semester. It includes instructions for the exam, a breakdown of questions with marks allocation, and various topics such as convolution, Fourier transforms, and system properties. The exam is scheduled for January 17, 2024, and consists of multiple questions requiring theoretical explanations and calculations.

Uploaded by

krishbhavsar69
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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Seat No.: ________ Enrolment No.

___________

GUJARAT TECHNOLOGICAL UNIVERSITY


BE - SEMESTER–IV (NEW) EXAMINATION – WINTER 2023
Subject Code:3141005 Date:17-01-2024
Subject Name:Signal & Systems
Time:10:30 AM TO 01:00 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) Find discrete Convolution of following pairs of signals. 03
and x(n) = {1,3,5,7} and h(n) = {2,4,6,8}
(b) Prove Commutative property of Convolution. 04
(c) What is ROC with respect to z- transform? What are its properties? 07

Q.2 (a) Find the DFT of the sequence x(n) = {1, 1, -2, -2} 03
(b) Enlist frequency shifting and time differentiation properties of Fourier 04
transform. Prove any one of them.
(c) State the sampling theorem. Also explain the reconstruction of a signal from 07
its samples using interpolation.
OR
(c) Determine the Z – Transform & ROC of the following sequence 07
x(n) = (3)n u(n) - (2)n u(-n-1)

Q.3 (a) Explain Scaling property in the z -Domain. 03


(b) State Dirichlet condition for Fourier Series Representation 04
(c) Determine the convolution sum of two sequences using graphical method 07
x(n) = {1, 4, 3, 2}; h(n) = {1, 3, 2, 1}
↑ ↑
OR
Q.3 (a) Find even and odd parts of 𝑥(𝑡)=𝑢(𝑡). 03
(b) Bring out difference between DFT and Fourier Transform (FT). 04
(c) Explain following property for the system 07
y(t) = 10 x(t) + 5.
(i) Linearity (ii) Time-invariance (iii) Causality (iv) Dynamicity

Q.4 (a) Explain the trigonometric Fourier series. 03


(b) Define energy and power. Hence, define energy signal and power signal. 04
(c) Calculate the DFT of a sequence 𝑥[𝑛]={1,1,0,0} and check the validity of 07
DFT by calculating its IDFT.
OR
Q.4 (a) Explain the Differentiation property of Z-Transform. 03
(b) Determine whether the following system with impulse response 04
h(t) = e-3 t u(t) is stable or not.
(c) Find the Fourier series coefficients for the continuous time periodic signal 07
x(t) = 1.5 for 0 ≤ t < 1
= -1.5 for 1 ≤ t < 2
with fundamental frequency W0 = π.

1
Q.5 (a) State and prove a condition for a discrete time LTI system to be stable. 03
(b) Find the natural response of the system described by difference equation 04
y(n) – 1.5 y(n - 1) + 0.5 y(n - 2) = x(n) ; y(-1) = 1; y(-2) = 0.
(c) Obtain the Fourier Transform of following signals: 07
1. 𝑥(𝑡) = cos𝜔0𝑡
2. 𝑥(𝑡) = sin𝜔𝑐𝑡 𝑢(𝑡)
OR
Q.5 (a) Explain relation between Fourier transform and z transform using necessary 03
equations.
(b) Prove that DT LTI system is causal if and only if h(n) = 0 for n < 0. 04
(c) Find whether the given signals are periodic or not? If yes, give its fundamental 07
period.
(i) x(t) = 3 sin 200πt + 4 cos 100t
(ii) x(n) = e j (π / 2) n
*********

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