The system shown below contains two linear shift-invariant subsystems with unit sample responses h₁ [n] and h₂ [n], in cascade. x (n) hy (n) hy (n) 19 0 w(n) 0 h₂ (n) = h₂ (n) = 8 (n) 8 (n-3) -1 (.8) u (n) y (n) (a) Let x[n] = u[n]. Find and sketch ya[n] by first convolving x[n] with h₁ [n] and then convolving that result with h₂ [n], i.e. Ya[n] = [x[n] * h₁[n]] * h₂ [n] (b) Again let x[n] = u[n]. Find and sketch y₁ [n] by convolving x[n] with the result of convolving h₁ [n] and h₂ [n], i.e.
The system shown below contains two linear shift-invariant subsystems with unit sample responses h₁ [n] and h₂ [n], in cascade. x (n) hy (n) hy (n) 19 0 w(n) 0 h₂ (n) = h₂ (n) = 8 (n) 8 (n-3) -1 (.8) u (n) y (n) (a) Let x[n] = u[n]. Find and sketch ya[n] by first convolving x[n] with h₁ [n] and then convolving that result with h₂ [n], i.e. Ya[n] = [x[n] * h₁[n]] * h₂ [n] (b) Again let x[n] = u[n]. Find and sketch y₁ [n] by convolving x[n] with the result of convolving h₁ [n] and h₂ [n], i.e.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![The system shown below contains two linear shift-invariant subsystems with unit sample responses
h₁ [n] and h₂ [n], in cascade.
x (n)
hy (n)
0
w(n)
h₁ (n) = 6(n) - 8 (n − 3)
1
h₂ (n) =
+!
0
h₂ (n)
-1
(.8) u (n)
y (n)
(a) Let x[n] = u[n]. Find and sketch ya [n] by first convolving x[n] with h₁ [n] and then convolving
that result with h₂ [n], i.e.
Ya[n] = [x[n] * h₁[n]] * h₂[n]
(b) Again let x[n] = u[n]. Find and sketch y₁ [n] by convolving x[n] with the result of convolving
h₁ [n] and h₂ [n], i.e.
y₁ [n] = x[n] * [h₁ [n] *h₂[n]]
(c) What convolution property does this demonstrate?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6bc06b6-0bfa-4388-bb17-1372d056aad3%2F9a0af742-04ba-4ea3-9ca3-e1fbdbc14ee7%2Fo6k2k5j_processed.png&w=3840&q=75)
Transcribed Image Text:The system shown below contains two linear shift-invariant subsystems with unit sample responses
h₁ [n] and h₂ [n], in cascade.
x (n)
hy (n)
0
w(n)
h₁ (n) = 6(n) - 8 (n − 3)
1
h₂ (n) =
+!
0
h₂ (n)
-1
(.8) u (n)
y (n)
(a) Let x[n] = u[n]. Find and sketch ya [n] by first convolving x[n] with h₁ [n] and then convolving
that result with h₂ [n], i.e.
Ya[n] = [x[n] * h₁[n]] * h₂[n]
(b) Again let x[n] = u[n]. Find and sketch y₁ [n] by convolving x[n] with the result of convolving
h₁ [n] and h₂ [n], i.e.
y₁ [n] = x[n] * [h₁ [n] *h₂[n]]
(c) What convolution property does this demonstrate?
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