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Consider a discrete-time LTI system described by the following time-domain relationship, where x[n] is the system input and y[n] is the system output. 1 y[n] = x[n] + (x[n − 1] + x[n + 1]) a) Is the system causal? Why or why not? b) Find the frequency response of the system H(w) : = c) Plot the frequency response H(w) over the frequency range -2π ≤ w ≤ 2π. Is the frequency response periodic in frequency? d) Find the output signal y[n] if the input signal is x [n] Y(w) X(w) = ejлn

Consider a discrete-time LTI system described by the following time-domain relationship, where x[n] is the system input and y[n] is the system output. 1 y[n] = x[n] + (x[n − 1] + x[n + 1]) a) Is the system causal? Why or why not? b) Find the frequency response of the system H(w) : = c) Plot the frequency response H(w) over the frequency range -2π ≤ w ≤ 2π. Is the frequency response periodic in frequency? d) Find the output signal y[n] if the input signal is x [n] Y(w) X(w) = ejлn

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Please answer part D. Thank you!

Consider a discrete-time LTI system described by the following time-domain relationship, where x[n] is the system input and y[n] is the system output. 1 y[n] = x[n] + (x[n − 1] + x[n + 1]) a) Is the system causal? Why or why not? b) Find the frequency response of the system H(w): c) Plot the frequency response H(w) over the frequency range -2π ≤ w ≤ 2π. Is the frequency response periodic in frequency? d) Find the output signal y[n] if the input signal is x [n] = Y(w) X(w) = ejлn
Transcribed Image Text:Consider a discrete-time LTI system described by the following time-domain relationship, where x[n] is the system input and y[n] is the system output. 1 y[n] = x[n] + (x[n − 1] + x[n + 1]) a) Is the system causal? Why or why not? b) Find the frequency response of the system H(w): c) Plot the frequency response H(w) over the frequency range -2π ≤ w ≤ 2π. Is the frequency response periodic in frequency? d) Find the output signal y[n] if the input signal is x [n] = Y(w) X(w) = ejлn
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