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A discrete-time system with input[n] and output y[n] is governed by y[n+1] − 0.75y[n] = x[n + 1] and the input x[n] = cos(nn). In the steady state, y[n] will have the minimum amplitude close to when Ω = π.

A discrete-time system with input[n] and output y[n] is governed by y[n+1] − 0.75y[n] = x[n + 1] and the input x[n] = cos(nn). In the steady state, y[n] will have the minimum amplitude close to when Ω = π.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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A discrete-time system with input \( x[n] \) and output \( y[n] \) is governed by \[ y[n+1] - 0.75y[n] = x[n+1] \] and the input \( x[n] = \cos(\Omega n) \). In the steady state, \( y[n] \) will have the minimum amplitude close to \_\_ when \( \Omega = \pi \).
Transcribed Image Text:A discrete-time system with input \( x[n] \) and output \( y[n] \) is governed by \[ y[n+1] - 0.75y[n] = x[n+1] \] and the input \( x[n] = \cos(\Omega n) \). In the steady state, \( y[n] \) will have the minimum amplitude close to \_\_ when \( \Omega = \pi \).
Expert Solution
Step 1: Formulating the Problem

Given: 

 

We need to find the steady-state value of  when .

Guessing the Steady-State Solution

For the given input, we guess the solution of the form: 

steps

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