Question

Download Solution PDF

Let u|n| be the unit-step signal and . The region of convergence of z-transform of x[n] is

This question was previously asked in
ESE Electronics 2014 Paper 1: Official Paper
Attempt in App
View all UPSC IES Papers >

Answer (Detailed Solution Below)

Option 3 :
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

Concept:

ROC IzI > IaI

Analysis:

Individual ROCs are IzI > () and IzI > ()

For write ROC for the causal system by default.

Hence common ROC for the causal system will be:

IzI > ()

Download Solution PDF
Latest UPSC IES Updates

Last updated on Jul 2, 2025

-> ESE Mains 2025 exam date has been released. As per the schedule, UPSC IES Mains exam 2025 will be conducted on August 10. 

-> UPSC ESE result 2025 has been released. Candidates can download the ESE prelims result PDF from here.

->  UPSC ESE admit card 2025 for the prelims exam has been released. 

-> The UPSC IES Prelims 2025 will be held on 8th June 2025.

-> The selection process includes a Prelims and a Mains Examination, followed by a Personality Test/Interview.

-> Candidates should attempt the UPSC IES mock tests to increase their efficiency. The UPSC IES previous year papers can be downloaded here.

Exams Tests Super Practice

More Properties of Region of Convergence Questions

Q1.The region of convergence of the sequence \(x[n]=\left(\frac{-1}{3}\right)^nu[n]-\left(\frac{1}{2}\right)^nu[-n-1]\) is
Q2.Let u|n| be the unit-step signal and \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}u\left[ n \right] + {\left( { - \frac{1}{3}} \right)^n}u\left[ n \right]\). The region of convergence of z-transform of x[n] is
Q3.Let \(x\left[ n \right]={\left( { - \frac{1}{9}} \right)^n}u\left[ n \right] - {\left( { - \frac{1}{3}} \right)^n}u\left[ { - n - 1} \right]\). The Region of convergence (ROC) of the z-transform
Q4.Consider a signal \(x\left[ n \right] = {\left( {\frac{1}{2}} \right)^n}1\left[ n \right]\), where 1[n] = 0 if n < 0, and 1[n] = 1 if n ≥ 0. The z-transform of x[n - k], k > 0 is \(\frac{{{z^{ - k}}}}{{1 - \frac{1}{2}\;{z^{ - 1}}}}\) with region of convergence being

More Z Transform Questions

Q1.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q2.What is the formula of finding the final value of any time varying function f(t)?
Q3.The z-transform of the impulse response of a causal LTI system is H(z) = \(\frac{1}{2}\frac{z^{-1}}{z^{-2} - 4.5z^{-1 }+5}\) .What is an input x(n) that would produce the output y(n) = u(-n) + (0.5)n u(n)? \(\frac{1}{2}\frac{z^-1}{z^-2 - 4.5z^-1 +5}\)12z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+12z−1z−2−4⋅5z−1+12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+5 12z−1z−2−4⋅5z−1+5
Q4.The 𝑍-transform of a discrete signal 𝑥[𝑛] is \(\rm X(z)=\frac{4z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}\) with ROC = R. Which one of the following statements is true?
Q5.The z transform of e−t sampled at 10 Hz will be:
Q6.Consider the transfer function \(\rm H_c(s)=\frac{1}{(s+1)(s+3)}\) Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function  Hd(z). Then Hd(z) is _______
Q7.Consider a signal x[n] = 2n u [n] having Z Transform as X (z) with ROC R. The Inverse Z Transform for X(2z) will be:
Q8.For an LTI system, the transfer function is \(H(z) = \frac{z}{{\left( {z - 0.2} \right)\left( {z - 0.5} \right)}};|z| > 0.5\), the system is ______ and _______.
Q9.If an LTI system with the transfer function H(z) = 1 + 2z-1 is excited with input x (n) = {3, 4}, compute the output of the system.
Q10.For a casual LTI system the impulse response is \(h(n)= \left\{ {\mathop 1\limits_ \uparrow ,2,1,3} \right\}\). What will be the system difference equation?
Suggested Test Series
View All >
UPSC ESE (IES) Civil Mock Test Series
116 Total Tests with 1 Free Tests
Start Free Test
UPSC ESE (IES) Electrical Mock Test Series
68 Total Tests with   0 Free Tests
Start Free Test

UPSC IES Important Links

ResultHall TicketEligibilitySalary and Job ProfileExam PatternECE Syllabus

More Signals and Systems Questions

Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.What type of distortion occurs if a signal that contains frequency components up to 15 kHz is sampled using 20 kHz?
Q4.Which one of the following systems described by the following input-output relations is time invariant ? 
Q5.The equation for voltage waveform v(t) shown below is (where u(t) is unit step input) :
Q6.A continuous-time signal x(t) is defined as : \(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\) The energy of signal x(t) is : 
Q7.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q8.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q9.Which one of the following is the correct relation ? (a > 0) 
Q10.What is the formula of finding the final value of any time varying function f(t)?
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
support@testbook.com
Toll Free:1800 833 0800
Office Hours: 10 AM to 7 PM (all 7 days)
Company
About usCareers We are hiringTeach Online on TestbookPartnersMediaSitemap
Products
Test SeriesTestbook PassOnline CoursesOnline VideosPracticeBlogRefer & EarnBooks
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Hot Links： teen patti customer care number teen patti 51 bonus teen patti master gold download