pLease help me for the question in the image 5) Consider the system with the following input-output relation with x[n] and y[n] being input andoutput respectively.y[n] = Even{x[n – 1]}Determine whether the system is memoryless, time invariant, linear, causal and stable.

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Engineering

Computer Science

pLease help me for the question in the image

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

pLease help me for the question in the image

5) Consider the system with the following input-output relation with x[n] and y[n] being input and
output respectively.
y[n] = Even{x[n – 1]}
Determine whether the system is memoryless, time invariant, linear, causal and stable.

Expert Solution

Step 1

y[n]=Even{x[n-1]} = 1/2 (x[n-1] + x[-1-n])

x[n+N] ---> y[n+N]

So the signal is time invariant.

x1+x2 --> y1+y2 , and a.x1 --> a.y1

So the signal is linear.

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