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% . . 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

Database System Concepts
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
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% . . 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
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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