d) x(n) = ucn) - U(n-2)
Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Needs answer only part 4 plzz
Transcribed Image Text:Find the z-transform for, the given xcm a) {1,2,3,2-2 b) x(n) = {3, 2, -1, -4,j} x(n) = {1, 2, - 1,2,3} d
)x(n) = v(n) - v(n - 2)
Find
and Roc
the 2-transform for the given xen,
{1,2,3,2}
2
a) x (n) =
b)
x (n) = { 2₁ 2₁ -1₁ -41 1}
T
c) x(n) =
d) x (n) =
{ ₁, 2, -1, 2, 3}
↑
ucn) - U(n-2)
![Given:
a) x[n] = {1, 2, 3, 2}
b) x[n] = {3, 2,-1,-4, 1}
c) x[n] = {1, 2, 1, 2, 3)
we need to find z-transform and ROC of above
signals.
Step 2: Finding Z-transform and ROC:
a)
x[n] = {1, 2, 3, 2},
As the signal varies from n=0 to n=3,
Z-transform,
X(z)= Σx[n]z",
3
n=0
→X(z)=x[0]+x[1]z¯¹+x[2]z−²+x[3]z-³,
⇒X(z)=1+2z1+3z-2+2z-3,
2
1 + ²/3 + 2/2 + 1/3 ; ROC: |Z| > 0
⇒X(z)=1+
b)
x[n] = {3, 2, 1, −4, 1}
As the signal varies from n=-4 to n=0,
Z-transform,
0
X(z)=x[n]z¯n,
n=-4
⇒X(z)=x[4]z + x[−3]z³+x[−2]z²+x[-1]z¹+x[0],
⇒X(z)=3z4+2z³-z²-4z¹+1,
⇒X(z)=3z4+2z³-z²-4z+1; ROC: |Z| <∞
c)
x[n] = {1, 2, 1, 2, 3)
As the signal varies from n=-2 to n=2,
Z-transform,
2
X(z)= Σ x[n]z¯n,
n=-2
⇒X(z)=x[-2]z4+x[−1]z³+x[0]+x[1]z−¹+x[2]z¯²,
⇒X(z)=z4+2z³-1+2z-¹+3z-²,
⇒X(z)=z4+2z³-1++; ROC:0<|z|<∞
3
Z z²](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdd2a86ab-5eca-44a1-8fbc-cef85722edcd%2F632cea0d-7353-4ceb-b1c6-69b6016d3e6d%2F02e1d66_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Given:
a) x[n] = {1, 2, 3, 2}
b) x[n] = {3, 2,-1,-4, 1}
c) x[n] = {1, 2, 1, 2, 3)
we need to find z-transform and ROC of above
signals.
Step 2: Finding Z-transform and ROC:
a)
x[n] = {1, 2, 3, 2},
As the signal varies from n=0 to n=3,
Z-transform,
X(z)= Σx[n]z",
3
n=0
→X(z)=x[0]+x[1]z¯¹+x[2]z−²+x[3]z-³,
⇒X(z)=1+2z1+3z-2+2z-3,
2
1 + ²/3 + 2/2 + 1/3 ; ROC: |Z| > 0
⇒X(z)=1+
b)
x[n] = {3, 2, 1, −4, 1}
As the signal varies from n=-4 to n=0,
Z-transform,
0
X(z)=x[n]z¯n,
n=-4
⇒X(z)=x[4]z + x[−3]z³+x[−2]z²+x[-1]z¹+x[0],
⇒X(z)=3z4+2z³-z²-4z¹+1,
⇒X(z)=3z4+2z³-z²-4z+1; ROC: |Z| <∞
c)
x[n] = {1, 2, 1, 2, 3)
As the signal varies from n=-2 to n=2,
Z-transform,
2
X(z)= Σ x[n]z¯n,
n=-2
⇒X(z)=x[-2]z4+x[−1]z³+x[0]+x[1]z−¹+x[2]z¯²,
⇒X(z)=z4+2z³-1+2z-¹+3z-²,
⇒X(z)=z4+2z³-1++; ROC:0<|z|<∞
3
Z z²
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