4. For discrete time signal x[n] defined as below, x[n]= {3, 0, 0, 0, 3} (a) Find DTFT X(e'®) and sketch its magnitude | X(e®) | over -n< @ < T. (b) Perform simple averaging with window width = 3, and sketch the result y[n]. (c) Let H(e") be the frequency response of the LTI system that corresponds to the simple averaging performed in (b). Express Y(e") (=DTFT of y[n]) in terms of X(ei") and H(e") and prove the expression.

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
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For discrete time signal x[n] defined as below.

4. For discrete time signal x[n] defined as below,
x[n]= {3, 0, 0, 0, 3}
(a) Find DTFT X(e®) and sketch its magnitude | X(e®) | over -t < @ < t.
(b) Perform simple averaging with window width = 3, and sketch the result y[n].
(c) Let H(e") be the frequency response of the LTI system that corresponds to the simple
averaging performed in (b). Express Y(ej®) (=DTFT of y[n]) in terms of X(e") and H(e")
and prove the expression.
Transcribed Image Text:4. For discrete time signal x[n] defined as below, x[n]= {3, 0, 0, 0, 3} (a) Find DTFT X(e®) and sketch its magnitude | X(e®) | over -t < @ < t. (b) Perform simple averaging with window width = 3, and sketch the result y[n]. (c) Let H(e") be the frequency response of the LTI system that corresponds to the simple averaging performed in (b). Express Y(ej®) (=DTFT of y[n]) in terms of X(e") and H(e") and prove the expression.
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