2. A discrete-time filter is given as: Y[z] z+¹-z-1 H[z] X[z] 2 a. Write the difference equation that describes y[n]. Use the tables provided below as - necessary. b. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer. c. What is the DC gain of H[z]? d. Using the difference equation from part (a), calculate the output y[n] given the following input signal: x[n] = 48[n] + 28[n 1] + 48[n − 2] + 18[n − 3] Only calculate the output for -2 ≤n≤ +5. e. Sketch a plot of x[n] and y[n].
2. A discrete-time filter is given as: Y[z] z+¹-z-1 H[z] X[z] 2 a. Write the difference equation that describes y[n]. Use the tables provided below as - necessary. b. Does the system have an infinite impulse response (IIR) or finite impulse response (FIR)? Justify your answer. c. What is the DC gain of H[z]? d. Using the difference equation from part (a), calculate the output y[n] given the following input signal: x[n] = 48[n] + 28[n 1] + 48[n − 2] + 18[n − 3] Only calculate the output for -2 ≤n≤ +5. e. Sketch a plot of x[n] and y[n].
Introductory Circuit Analysis (13th Edition)
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Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Answer parts d and e, already posted abc
![2. A discrete-time filter is given as:
Y[z]
z¹-z-¹
z+1
Z
H[z]=
X[z]
2
a. Write the difference equation that describes y[n]. Use the tables provided below as
necessary.
b. Does the system have an infinite impulse response (IIR) or finite impulse response
(FIR)? Justify your answer.
What is the DC gain of H[z]?
Using the difference equation from part (a), calculate the output y[n] given the
following input signal:
x[n] = 48[n] + 28[n 1] + 48[n-2] + 18[n-3]
c.
d.
DESDE
Only calculate the output for −2 ≤ n ≤ +5.
e. Sketch a plot of x[n] and y[n].
4](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8be12032-d26f-4088-913e-abb4eb227e0d%2Ff76f2ce4-2dfd-42ae-b51d-6f717306ccd3%2Fzdcd1f4_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. A discrete-time filter is given as:
Y[z]
z¹-z-¹
z+1
Z
H[z]=
X[z]
2
a. Write the difference equation that describes y[n]. Use the tables provided below as
necessary.
b. Does the system have an infinite impulse response (IIR) or finite impulse response
(FIR)? Justify your answer.
What is the DC gain of H[z]?
Using the difference equation from part (a), calculate the output y[n] given the
following input signal:
x[n] = 48[n] + 28[n 1] + 48[n-2] + 18[n-3]
c.
d.
DESDE
Only calculate the output for −2 ≤ n ≤ +5.
e. Sketch a plot of x[n] and y[n].
4
![Some helpful z transforms:
Signal
1. 8[n]
2. u[n]
3. -u[-n-1]
4. 8[nm]
5. au[n]
6.-0"u[-n-1]
7. na" u[n]
8. -na"u-n-1]
9. [cos won]u[n]
10. [sin won]u[n]
11. [ cos won]u[n]
12. [r sin won]u[n]
Transform
1
-6 -6
2-m
1-az
1
1-az-1
92-1
(1-02-1)2
uz
(1-a2-1)²
1-[cos wo] 2-1
1-[2 cos wo]z-1+2−2
[(sin wolz-1
1-2 cos wp]z-1+z
ROC
1-[2r cos wo]z ¹+r²2
[r sin wo]=-1
1-[2r cos wo]2
All 2
> 1
|2|< 1
All z except
0 (if m > 0) or
∞ (if m < 0)
| 2 | > |a|
|z| < |a|
z> a
|2| < |a|
2 > 1
2 > 1
1-[r cos wo]z-1
1-2r cos 02-1+7²2-2 |2|>r
T
1+7²2 2. 2>r](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8be12032-d26f-4088-913e-abb4eb227e0d%2Ff76f2ce4-2dfd-42ae-b51d-6f717306ccd3%2Ffqt6k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Some helpful z transforms:
Signal
1. 8[n]
2. u[n]
3. -u[-n-1]
4. 8[nm]
5. au[n]
6.-0"u[-n-1]
7. na" u[n]
8. -na"u-n-1]
9. [cos won]u[n]
10. [sin won]u[n]
11. [ cos won]u[n]
12. [r sin won]u[n]
Transform
1
-6 -6
2-m
1-az
1
1-az-1
92-1
(1-02-1)2
uz
(1-a2-1)²
1-[cos wo] 2-1
1-[2 cos wo]z-1+2−2
[(sin wolz-1
1-2 cos wp]z-1+z
ROC
1-[2r cos wo]z ¹+r²2
[r sin wo]=-1
1-[2r cos wo]2
All 2
> 1
|2|< 1
All z except
0 (if m > 0) or
∞ (if m < 0)
| 2 | > |a|
|z| < |a|
z> a
|2| < |a|
2 > 1
2 > 1
1-[r cos wo]z-1
1-2r cos 02-1+7²2-2 |2|>r
T
1+7²2 2. 2>r
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