Signal x[n] is periodic with fundamental period N = 4. It is given by x[n] = (¹ primary interval 0 ≤ n ≤ 3. It is applied as an input to a causal LTI system given by: over its H(z) = 3z²z+1 z²z+1/3 a. Find both the magnitude and phase of the frequency response of the system and comment on your results. b. Determine the Cx),0 ≤ k ≤ 3 of x[n]. C. Determine the C,0 ≤ k ≤ 3 of y[n].

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Signal x[n] is periodic with fundamental period N = 4. It is given by x[n] = (¹
primary interval 0 ≤ n ≤ 3. It is applied as an input to a causal LTI system given by:
over its
H(z) :
=
3z² - z+1
z² − z + 1/3
a.
Find both the magnitude and phase of the frequency response of the system and comment
on your results.
b. Determine the C),0 ≤ k ≤ 3 of x[n].
c. Determine the C),0 ≤ k ≤ 3 of y[n].
d. Calculate C(x) and C.
e. Compute the steady-state response yss [n].
Transcribed Image Text:Signal x[n] is periodic with fundamental period N = 4. It is given by x[n] = (¹ primary interval 0 ≤ n ≤ 3. It is applied as an input to a causal LTI system given by: over its H(z) : = 3z² - z+1 z² − z + 1/3 a. Find both the magnitude and phase of the frequency response of the system and comment on your results. b. Determine the C),0 ≤ k ≤ 3 of x[n]. c. Determine the C),0 ≤ k ≤ 3 of y[n]. d. Calculate C(x) and C. e. Compute the steady-state response yss [n].
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