Unit step response of the system described by difference equation y(n) + y(n - 1) = x(n) is

This question was previously asked in
ESE Electronics 2011 Paper 1: Official Paper
View all UPSC IES Papers >

Answer (Detailed Solution Below)

Option 1 :
Free
ST 1: UPSC ESE (IES) Civil - Building Materials
20 Qs. 40 Marks 24 Mins

Detailed Solution

Download Solution PDF

Concept:

1. Analysis of continuous-time LTI systems can be done using z-transforms.

It is a powerful mathematical tool to convert differential equations into algebraic equations.

2. The bilateral (two-sided) z-transform of a discrete-time signal x(n) is given as

3. The unilateral (one-sided) z-transform of a discrete-time signal x(n) is given as

4. Time shifting property of Z transform

x(n - 1) = z-1x(z)

5. Z transform of u(n)

Calculation:

Given,

y(n) + y(n-1) = x(n)  ----(1)

Now finding unit step response of equation (1) using above properties we get:

Hence option (1) is the correct answer.

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.

More Z Transform Questions

Hot Links: teen patti real cash game teen patti circle teen patti master list