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

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Physics

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Waves and Their Applications in Technologies for Information Transfer

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rectangular-and-triangular-pulse-function

Rectangular and Triangular Pulse Function

Единичная прямоугольная импульсная функция математически представлена прямоугольной функцией с центром в начале координат и высотой в одну единицу.
Эту функцию определяют два параметра: T, определяющий центральное положение импульса вдоль оси времени, и τ, определяющий длительность импульса.
В качестве примера можно привести прямоугольный импульс с амплитудой 5 В, длительностью 3 с и центром, расположенным в момент времени, равным 2 с. Этот импульс может быть выражен с помощью прямоугольной функции.
Синтез прямоугольного импульса включает в себя графическую демонстрацию последовательного сложения двух сдвинутых по времени ступенчатых функций.
В общих чертах, единичная прямоугольная функция всегда может быть выражена с помощью единичной ступенчатой функции.
Единичная треугольная функция математически выражается через треугольную функцию. Он имеет единичную высоту и центрирован в начале координат.
Экземпляр представляет собой треугольный импульс с центром в время, равное 3 с, с амплитудой 2 и шириной 2 с. Чтобы нарисовать треугольный импульс, замените каждое t на t-3 и установите ширину, равную двум. Определенный сигнал демонстрируется графически.

Функция прямоугольного и треугольного импульса

Единичная функция прямоугольного импульса математически представлена ​​прямоугольной функцией с центром в начале координат и высотой, равной единице. Эта функция определяется двумя параметрами: T, который определяет центральное местоположение импульса по оси времени, и τ, который определяет длительность импульса.

Например, рассмотрим прямоугольный импульс с амплитудой 5 В, длительностью 3 секунды и центром в t=2 секунды. Этот импульс можно выразить с помощью прямоугольной функции, записанной как

<img alt="Equation1" src="/files/ftp_upload/16041/16041_PT%20EQUATION_1.svg" style="text-align: center; height: 36px;">

Синтез прямоугольного импульса можно продемонстрировать графически, последовательно добавив две сдвинутые во времени ступенчатые функции. В общих чертах, единичная прямоугольная функция всегда может быть выражена с помощью единичной ступенчатой ​​функции следующим образом:

<img alt="Equation2" src="/files/ftp_upload/16041/16041_PT%20EQUATION_2.svg" style="text-align: center; height: 36px;">

Единичная треугольная функция математически выражается через треугольную функцию. Она имеет единичную высоту и центрирована в начале координат. Например, рассмотрим треугольный импульс с центром в t=3 секунды, с величиной 2 и шириной 2 секунды. Чтобы выразить этот треугольный импульс, замените каждую t на t−3 и установите ширину равной 2. Определенный таким образом сигнал можно записать как,

<img alt="Equation3" src="/files/ftp_upload/16041/16041_PT%20EQUATION_3.svg" style="text-align: center; height: 36px;">

Эту функцию треугольного импульса можно проиллюстрировать графически, показав, как ее высота достигает 2 в центре и сужается до нуля по краям, охватывая общую ширину 2 секунды.

Как единичные прямоугольные, так и треугольные функции являются основополагающими в обработке сигналов для представления различных форм волн и используются во многих приложениях для моделирования и анализа сигналов и систем. Эти функции необходимы для понимания более сложного поведения и более сложных операций с сигналами.

Единичная прямоугольная импульсная функция математически представлена прямоугольной функцией с центром в начале координат и высотой в одну единицу.
Два...

Education

JoVE Core

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Unit 1

Раздел 1

Introduction to Signals and Systems

Введение в сигналы и системы

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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

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signal and system

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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...

exponential and sinusoidal signals

Complex Exponentials in Signal Behavior

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key terms and concepts

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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