% . . 19 LTE1 ۱۲:۲۰ يحتوي هذا المستند على الحبر والاشكال والصور غير المقروء.... 3. Mathematical Example Example: Compute the Z-transform of x[n] = (0.5)"u[n], where u[n] is the unit step function Solution: The Z-transform is given by: 00 X(z) = (0.5)"z" n=0 Factoring z-n 00 X(=) = Σ (0-5)** This is a geometric series with the sum: 1 X(z) 0.5' for [z] > 0.5 1- Z Simplifying Z X(z) ROC: |z❘ > 0.5 z-0.5 4. Engineering Application Application in Digital Signal Processing (DSP): Digital Filter Design One practical application of the Z-transform is in the design of digital filters used in audio processing, telecommunications, and image processing. Example: Low-Pass Filter Design Consider a simple discrete-time system described by the difference equation: III O
% . . 19 LTE1 ۱۲:۲۰ يحتوي هذا المستند على الحبر والاشكال والصور غير المقروء.... 3. Mathematical Example Example: Compute the Z-transform of x[n] = (0.5)"u[n], where u[n] is the unit step function Solution: The Z-transform is given by: 00 X(z) = (0.5)"z" n=0 Factoring z-n 00 X(=) = Σ (0-5)** This is a geometric series with the sum: 1 X(z) 0.5' for [z] > 0.5 1- Z Simplifying Z X(z) ROC: |z❘ > 0.5 z-0.5 4. Engineering Application Application in Digital Signal Processing (DSP): Digital Filter Design One practical application of the Z-transform is in the design of digital filters used in audio processing, telecommunications, and image processing. Example: Low-Pass Filter Design Consider a simple discrete-time system described by the difference equation: III O
C++ for Engineers and Scientists
4th Edition
ISBN:9781133187844
Author:Bronson, Gary J.
Publisher:Bronson, Gary J.
Chapter4: Selection Structures
Section: Chapter Questions
Problem 14PP
Related questions
Question
![% . . 19
LTE1
۱۲:۲۰
يحتوي هذا المستند على الحبر والاشكال والصور غير المقروء....
3. Mathematical Example
Example: Compute the Z-transform of x[n] = (0.5)"u[n], where u[n] is the unit
step function
Solution: The Z-transform is given by:
00
X(z) = (0.5)"z"
n=0
Factoring z-n
00
X(=) = Σ (0-5)**
This is a geometric series with the sum:
1
X(z)
0.5'
for [z] > 0.5
1-
Z
Simplifying
Z
X(z)
ROC: |z❘ > 0.5
z-0.5
4. Engineering Application
Application in Digital Signal Processing (DSP): Digital Filter Design
One practical application of the Z-transform is in the design of digital filters used in
audio processing, telecommunications, and image processing.
Example: Low-Pass Filter Design
Consider a simple discrete-time system described by the difference equation:
III
O](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5290b12-0bfe-4e36-a07c-a2a5184648f7%2F86d89825-ccc3-4708-9239-182bdb630057%2Fyoocjdg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:% . . 19
LTE1
۱۲:۲۰
يحتوي هذا المستند على الحبر والاشكال والصور غير المقروء....
3. Mathematical Example
Example: Compute the Z-transform of x[n] = (0.5)"u[n], where u[n] is the unit
step function
Solution: The Z-transform is given by:
00
X(z) = (0.5)"z"
n=0
Factoring z-n
00
X(=) = Σ (0-5)**
This is a geometric series with the sum:
1
X(z)
0.5'
for [z] > 0.5
1-
Z
Simplifying
Z
X(z)
ROC: |z❘ > 0.5
z-0.5
4. Engineering Application
Application in Digital Signal Processing (DSP): Digital Filter Design
One practical application of the Z-transform is in the design of digital filters used in
audio processing, telecommunications, and image processing.
Example: Low-Pass Filter Design
Consider a simple discrete-time system described by the difference equation:
III
O
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