P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(2) as a rational function in z-¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. 1. x(n) = 28(n − 2) + 3u(n − 3).
P1) Determine the z-transform of the following sequences using the z-transform table and the z-transform properties. Express X(2) as a rational function in z-¹. Verify your results using MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot. 1. x(n) = 28(n − 2) + 3u(n − 3).
Introductory Circuit Analysis (13th Edition)
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If you cant do the matlab part its okay but i would appreciate it please determine the z transforms of the following signals in the image below by using the properties of z transform and common z transform pairs firstly that i also provided thank you
Transcribed Image Text:P1) Determine the z-transform of the following sequences using the z-transform table and the
z-transform properties. Express X(z) as a rational function in z¹. Verify your results using
MATLAB. Indicate the region of convergence in each case, and provide a pole-zero plot.
-
1. x(n) = 28(n − 2) + 3u(n − 3).
2. x(n) = 3(0.75)" cos(0.3лn)u(n) + 4(0.75)" sin(0.3)u(n)
3. x(n) = n sin()u(n) + (0.9)"u(n − 2).
4. x(n) =
n² (2/3)u(n-1).
-
![3. SOME COMMON Z-TRANSFORM PAIRS
2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM
Signal
Transform
1. Linearity:
1. 6[n]
1
ROC
All z
Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC
2. u[n]
(4.4)
3. -u-n-1]
|z| > 1
|z| < 1
2. Sample shifting:
4. 5[n—m]
2x (n-no)] =20X(2); ROC: ROC
(4.5)
3. Frequency shifting:
5. au[n]
az
All z except
0 (if m> 0) or
x (if m < 0)
|z| > |a|
Za" (n)] = X(); ROC: ROC, scaled by |a|
(4.6)
4. Folding:
6. —au[-n − 1]
7. nan u[n]
1
1-az
Zx(-n)] X (1/2); ROC: Inverted ROC
(4.7)
5. Complex conjugation:
Za(n)] X(); ROC: ROC
(4.8)
8. -nau[―n — 1]
9. [cos won]u[n]
10. [sin won]u[n]
11. [ cos won]u[n]
12. [ sin won]u[n]
92-1
(1-az-1)2
2-1
(1-02-132
1-[cos wo]-1
1-[2 cos wo]=-1+=-2
[sin wo]z-1
1-12 cos wo]z-1+2-2
1-[r cos wo]=-1
1-[2r cos wo]z=1+r²z-2
|z| < |a|
|z| > |a|
|z| < |a|
|z|> 1
|z| > 1
|z| > r
[rsin wolz-1
1-[2rcos wo]z=1+r²z=2
|=| > T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3b5d4c98-afbd-424f-9855-c5eac84955f5%2Fee852edf-dd79-4993-96c0-305cf0501186%2Ft1pw38b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. SOME COMMON Z-TRANSFORM PAIRS
2. IMPORTANT PROPERTIES OF THE Z-TRANSFORM
Signal
Transform
1. Linearity:
1. 6[n]
1
ROC
All z
Za1x1(n) + a2x2(n)] = a1X1(2)+ a2X2(2); ROC: ROC, ROC
2. u[n]
(4.4)
3. -u-n-1]
|z| > 1
|z| < 1
2. Sample shifting:
4. 5[n—m]
2x (n-no)] =20X(2); ROC: ROC
(4.5)
3. Frequency shifting:
5. au[n]
az
All z except
0 (if m> 0) or
x (if m < 0)
|z| > |a|
Za" (n)] = X(); ROC: ROC, scaled by |a|
(4.6)
4. Folding:
6. —au[-n − 1]
7. nan u[n]
1
1-az
Zx(-n)] X (1/2); ROC: Inverted ROC
(4.7)
5. Complex conjugation:
Za(n)] X(); ROC: ROC
(4.8)
8. -nau[―n — 1]
9. [cos won]u[n]
10. [sin won]u[n]
11. [ cos won]u[n]
12. [ sin won]u[n]
92-1
(1-az-1)2
2-1
(1-02-132
1-[cos wo]-1
1-[2 cos wo]=-1+=-2
[sin wo]z-1
1-12 cos wo]z-1+2-2
1-[r cos wo]=-1
1-[2r cos wo]z=1+r²z-2
|z| < |a|
|z| > |a|
|z| < |a|
|z|> 1
|z| > 1
|z| > r
[rsin wolz-1
1-[2rcos wo]z=1+r²z=2
|=| > T
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