Name: modeling pulses with rectangles and triangles
Uploaded: 2025-05-22T09:06:20.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

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South Carolina College and Career Ready Science Standards

High School

Physics

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Waves and Their Applications in Technologies for Information Transfer

P-PS4-5

rectangular-and-triangular-pulse-function

Rectangular and Triangular Pulse Function

يتم تمثيل وظيفة النبض المستطيل للوحدة رياضيا من خلال الوظيفة المستطيلة المتمركزة في الأصل بارتفاع وحدة واحدة.
تحدد معلمتان هذه الوظيفة: T ، تحدد الموقع المركزي للنبضة على طول المحور الزمني ، و τ ، تحديد مدة النبضة.
مثال على ذلك يمكن أن يكون نبضة مستطيلة بسعة 5 فولت ، ومدة 3 ثوان ومركز موجود في الوقت يساوي 2 ثانية. يمكن التعبير عن هذه النبضة باستخدام الدالة المستطيلة.
يتضمن تجميع النبضة المستطيلة العرض الرسومي لإضافة وظيفتين متتاليتين للخطوة متغيرة زمنيا.
بشكل عام ، يمكن دائما التعبير عن دالة مستطيلة الوحدة باستخدام وظيفة خطوة الوحدة.
يتم التعبير عن الدالة المثلثة للوحدة رياضيا عبر الدالة المثلثة. لها وحدة ارتفاع وتتركز في الأصل.
المثيل هو نبضة مثلثة متمركزة في وقت يساوي 3 ثوان ، بمقدار 2 وعرض 2 ثانية. لرسم نبضة مثلثة ، استبدل كل t ب t-3 واضبط العرض يساوي اثنين. يتم عرض الإشارة المحددة بيانيا.

دالة النبضة المستطيلة والمثلثية

<div style="direction: rtl;">
يتم تمثيل دالة النبضة المستطيلة الوحدوية رياضيًا بدالة مستطيلة مركزها الأصل بارتفاع وحدة واحدة. تُعرَّف هذه الدالة بواسطة معاملين: T، الذي يحدد موقع مركز النبضة على طول محور الزمن، وτ، الذي يحدد مدة النبضة.

على سبيل المثال، ضع في اعتبارك نبضة مستطيلة بسعة 5 فولت ومدة 3 ثوانٍ ومركزها t=2 ثانية. يمكن التعبير عن هذه النبضة باستخدام الدالة المستطيلة، المكتوبة على النحو التالي،

<img alt="Equation1" src="/files/ftp_upload/16041/16041_PT%20EQUATION_1.svg" style="text-align: center; height: 36px;">
يمكن توضيح تركيب النبضة المستطيلة بيانيًا عن طريق إضافة دالتين متتاليتين متحولتين زمنيًا. بشكل عام، يمكن دائمًا التعبير عن دالة مستطيلة وحدوية باستخدام دالة الخطوة الوحدوية على النحو التالي:

<img alt="Equation2" src="/files/ftp_upload/16041/16041_PT%20EQUATION_2.svg" style="text-align: center; height: 36px;">
يتم التعبير عن دالة المثلث الوحدوي رياضيًا من خلال الدالة المثلثية. لها ارتفاع وحدة ومركزها نقطة الأصل. على سبيل المثال، ضع في اعتبارك نبضة مثلثية مركزها t=3 ثوانٍ، بمقدار 2 وعرض 2 ثانية. للتعبير عن هذه النبضة المثلثية، استبدل كل t بـ t-3 واضبط العرض على 2. يمكن كتابة الإشارة المحددة على النحو التالي،

<img alt="Equation3" src="/files/ftp_upload/16041/16041_PT%20EQUATION_3.svg" style="text-align: center; height: 36px;">
يمكن توضيح دالة النبضة المثلثية هذه بيانيًا، مع توضيح كيف يصل ارتفاعها إلى 2 في المنتصف ويتناقص إلى الصفر عند الأطراف، ويمتد على عرض إجمالي يبلغ 2 ثانية.

تعتبر كل من الدالتين المستطيلة والمثلثة الوحدوية أساسيتين في معالجة الإشارات لتمثيل أشكال الموجات المختلفة وتستخدمان في تطبيقات متعددة لنمذجة وتحليل الإشارات والأنظمة. تعد هذه الدالتين ضروريتين لفهم سلوكيات وعمليات الإشارات الأكثر تعقيدًا.

</div>

يتم تمثيل وظيفة النبض المستطيل للوحدة رياضيا من خلال الوظيفة المستطيلة المتمركزة في الأصل بارتفاع وحدة واحدة.
اثنان...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Introduction to Signals and Systems

مقدمة في الإشارات والأنظمة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

modeling pulses with rectangles and triangles

Rectangular and triangular pulse functions are basic signal shapes used to model waveforms in signal processing. The rectangular pulse has a flat top and is centered at the origin with a height of one unit. It is described by two parameters: T, which gives the center location on the time axis, and τ, which sets the pulse duration.

A rectangular pulse can also represent a real signal with a chosen amplitude and length. For example, a pulse with a 5 V amplitude, a 3-second duration, and a center at t = 2 seconds can be written with the rectangular function. The same shape can be built graphically by adding two time-shifted step functions in sequence. In general, a unit rectangular function can be written using the unit step function.

The unit triangular function is another common pulse shape. It has unit height and is centered at the origin. For a triangular pulse centered at t = 3 seconds, with a magnitude of 2 and a width of 2 seconds, each t value is replaced with t − 3 and the width is set to 2.

A triangular pulse rises to its peak at the center and then falls to zero at the edges. In this example, the height reaches 2 at the center and spans a total width of 2 seconds. Rectangular and triangular functions are both important in signal processing because they help represent waveforms and support the modeling and analysis of signals and systems. They also provide a foundation for understanding more complex signal behavior and operations.

Modeling Pulses with Rectangles and Triangles

modeling-pulses-with-rectangles-and-triangles

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rectangular and triangular pulse function

Rectangular and triangular pulse functions are basic signal shapes used to model waveforms in signal processing. The rectangular pulse has a flat top and is centered at the origin with a height of one unit. It is described by two parameters: T, which gives the center location on the time axis, and τ, which sets the pulse duration. A rectangular pulse can also represent a real signal with a chosen amplitude and length. For example, a pulse with a 5 V amplitude, a 3-second duration, and a center...

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Learn how rectangular and triangular pulse functions model signals, use center and width parameters, and connect to step functions in signal processing.

Modeling Pulses with Rectangles and Triangles | JoVE K12

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Modeling Pulses with Rectangles and Triangles

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