Consider the causal discrete-time system described by the difference equation: y[n] + žy[n − 1] + ¹⁄y[n − 2] = x[n] Determine the system function H(z). 1 , ROC: 2 > 1/2 (1 + ½⁄z−¹)(1 + z−¹) ' 1 , ROC: |Z| 1/ (1-z-¹)(1-z-¹) ' Determine the impulse response h[n]. O[2(–})" –3(–3)"][n] O[(})" — (3)"]u[n] OK 1\n ( 1\]..[..]
Consider the causal discrete-time system described by the difference equation: y[n] + žy[n − 1] + ¹⁄y[n − 2] = x[n] Determine the system function H(z). 1 , ROC: 2 > 1/2 (1 + ½⁄z−¹)(1 + z−¹) ' 1 , ROC: |Z| 1/ (1-z-¹)(1-z-¹) ' Determine the impulse response h[n]. O[2(–})" –3(–3)"][n] O[(})" — (3)"]u[n] OK 1\n ( 1\]..[..]
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Consider the causal discrete-time system described by the difference equation:
![Consider the causal discrete-time system described by the difference equation:
y[n] + žy[n − 1] + {y[n − 2] = x[n]
-
Determine the system function H(z).
1
-, ROC: |Z| >
2 //
(1 + z−¹)(1+z−¹)'
1
, ROC: |Z| <=
*(1 + ½ z−¹)(1 +
z−¹)'
1
ROC: = < <=/
(1 − ½z-¹)(1 –
z−¹) '
1
, ROC: = <2</
(1 − ½ z−¹)(1 + z−¹)'
1
, ROC: = < < <=
(1 + z−¹)(1+z−¹)'
1
, ROC: 2 > //
(1 – ½ z−¹)(1 – z−¹) '
Determine the impulse response h[n].
O[2(–})" – 3(–3)"][n]
O[(})” _ (})"]u[n]
Ol(-})" -(-3)"]u[n]
O[3(})” – 2(})”]u[n]
O[2(})n – 3(})"]u[n]
-
O[3(–})" – 2(–3)"]un](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29afb542-cc51-47a6-bbab-4e59d0a7e24b%2Fea831d76-7e03-4fa1-8c0b-3c46d2ed5c16%2F7pvzqft_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the causal discrete-time system described by the difference equation:
y[n] + žy[n − 1] + {y[n − 2] = x[n]
-
Determine the system function H(z).
1
-, ROC: |Z| >
2 //
(1 + z−¹)(1+z−¹)'
1
, ROC: |Z| <=
*(1 + ½ z−¹)(1 +
z−¹)'
1
ROC: = < <=/
(1 − ½z-¹)(1 –
z−¹) '
1
, ROC: = <2</
(1 − ½ z−¹)(1 + z−¹)'
1
, ROC: = < < <=
(1 + z−¹)(1+z−¹)'
1
, ROC: 2 > //
(1 – ½ z−¹)(1 – z−¹) '
Determine the impulse response h[n].
O[2(–})" – 3(–3)"][n]
O[(})” _ (})"]u[n]
Ol(-})" -(-3)"]u[n]
O[3(})” – 2(})”]u[n]
O[2(})n – 3(})"]u[n]
-
O[3(–})" – 2(–3)"]un
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