Testbook Logo
Exams SuperCoaching Test Series Skill Academy
More
English
Hindi

Question

Download Solution PDF

The response of a linear, time-invariant, discrete time system to a unit step input u[n] is δ[n]. The system response to a ramp input n u[n] would be:

This question was previously asked in
ESE Electronics 2016 Paper I: Official Paper
Attempt Online
View all UPSC IES Papers >
  1. δ [n - 1]
  2. u [n - 1]
  3. n δ [n - 1]
  4. n u [n - 1]

Answer (Detailed Solution Below)

Option 2 : u [n - 1]
Free Tests
View all Free tests >
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
6.3 K Users
20 Questions 40 Marks 24 Mins
Start Now

Detailed Solution

Download Solution PDF

For x[n] = u[n], y[n] = δ[n]

First difference equation,

u[n] – u[n - 1] = δ[n]

y[n] = x[n] – x[n - 1]

For ramp input, x[n] = n u [n]

y[n] = n u [n] – (n - 1) u [n – 1]

= n u [n] – n u [n – 1] + u [n – 1]

= n [u[n] – u[n - 1]] + u [n - 1]

= n δ[n] + u [n - 1]

= 0 + u [n - 1]

⇒ y [n] = u [n - 1]

∴ The system response y[n] = u [n - 1]

Download Solution PDF
Latest UPSC IES Updates

Last updated on May 28, 2025

->  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.

More Discrete Time LTI Systems Questions

Q1.A system is defined by its impulse response h(n) = 2nu(n - 2). The system is
Q2.Which one of the following is correct for the given system ? y[n] = x[n] - x[n - 1]
Q3.A discrete time signal, which is both linear and time invariant has an impulse response is u[n]. What is the response of the system for an input δ[n - 4]? 
Q4.The response of a linear, time-invariant, discrete time system to a unit step input u[n] is δ[n]. The system response to a ramp input n u[n] would be:
Q5.Consider the discrete-time signal \(x\left( n \right) = {\left( {\frac{1}{3}} \right)^n}u\left( n \right),where\;u\left( n \right) = \left\{ {\begin{array}{*{20}{c}} {1,}&{n \ge 0}\\ {0,}&{n < 0} \end{array}} \right.\)  Define the signal y(n) ⇒ as y(n) = x(-n), -∞ < n < ∞ Then, \(\mathop \sum \limits_{n = - \infty }^\infty y\left( n \right)\) equals

More Linear Time Invariant Systems Questions

Q1.Which one of the following systems described by the following input-output relations is time invariant ? 
Q2.A continuous-time system that is initially at rest is described by \(\rm \frac{dy(t)}{dt}+3y(t)=2x(t)\), where 𝑥(𝑡) is the input voltage and 𝑦(𝑡) is the output voltage. The impulse response of the system is
Q3.Let 𝑥(𝑡) = 10 cos(10.5 𝑊𝑡) be passed through an LTI system having impulse response \(\rm h(t)=\pi \left(\frac{\sin Wt}{\pi t}\right)^2\cos 10Wt\). The output of the system is 
Q4.Rearrange the parts of the sentence in correct order. When grandfather first P: Showed me the pond world Q: Sat for an hour lazily R: He chose a dry place in the shade of S: An old peepul tree where we
Q5.Which of the following statements with respect to the stability of a control system is true? a. The roots of the characteristic equation are on the left half of the s-plane. b. The system is bounded input bounded output (BIBO) stable. c. Stability is independent of the input. d. The roots of the characteristic equation are on the left half of the s-plane and on the imaginary axis.
Q6.In a linear time invariant system, the time invariance condition describes a system in which a delay in the input causes-
Q7.Which one of the following statements is correct for the given system? \(y(n) = {x^2}(n) + \frac{1}{{{x^2}(n - 1)}}\)
Q8.The outputs of four systems (S1, S2, S3, and S4) corresponding to the input signal sin(t), for all time t, are shown in the figure. Based on the given information, which of the four systems is/are definitely NOT LTI (linear and time-invariant)?
Q9.Let an input x(t) = 2 sin(10πt) + 5 cos(15πt) + 7 sin(42πt) + 4 cos(45πt) is passed through an LTI system having an impulse response \(\rm h(t) = 2 \left( \frac{\sin (10 \pi t)}{\pi t} \right) \cos (40 \pi t)\) The output of the system is
Q10.Let a causal LTI system be governed by the following differential equation \(\rm y(t) + \frac{1}{4} \frac{dy}{dt} = 2x(t)\) where x(𝑡) and y(𝑡) are the input and output respectively. Its impulse response is
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) Prelims Paper 1 Mock Test Series
54 Total Tests with   1 Free Tests
Start Free Test

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)?
Important Exams
Super Coaching
Exams
Test Series
Previous Year Papers
Objective Questions
Testbook USA SAT Exam
Testbook USA ACT Exam
US College Admissions Guide
Testbook Edu Solutions Pvt. Ltd.
1st & 2nd Floor, Zion Building,
Plot No. 273, Sector 10, Kharghar,
Navi Mumbai - 410210
[email protected]
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
Our Apps
Follow us on
Copyright © 2014-2022 Testbook Edu Solutions Pvt. Ltd.: All rights reserved
User PolicyTermsPrivacy
Get Free Access Now
Hot Links： teen patti cash teen patti gold new version 2024 teen patti boss