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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Waves and Their Applications in Technologies for Information Transfer

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Rectangular and Triangular Pulse Function

A função de pulso retangular unitário é matematicamente representada pela função retangular centrada na origem com uma altura de uma unidade.
Dois parâmetros definem esta função: T, especificando a localização central do pulso ao longo do eixo do tempo, e τ, determinando a duração do pulso.
Um exemplo pode ser um pulso retangular com amplitude de 5V, duração de 3s e um centro localizado no tempo igual a 2s. Este pulso pode ser expresso usando a função retangular.
Sintetizar o pulso retangular envolve a demonstração gráfica da adição sequencial de duas funções de passo deslocadas no tempo.
Em termos gerais, uma função retangular unitária sempre pode ser expressa usando a função de passo unitário.
A função triangular unitária é expressa matematicamente através da função triangular. Tem altura unitária e está centrado na origem.
Uma instância é um pulso triangular centrado em um tempo igual a 3s, com uma magnitude de 2 e uma largura de 2s. Para esboçar um pulso triangular, substitua cada t por t-3 e defina a largura igual a dois. O sinal definido é demonstrado graficamente.

função de pulso retangular e triangular

A função de pulso retangular unitária é matematicamente representada por uma função retangular centrada na origem com uma altura de uma unidade. Esta função é definida por dois parâmetros: T, que especifica a localização central do pulso ao longo do eixo do tempo, e τ, que determina a duração do pulso.

Por exemplo, considere um pulso retangular com uma amplitude de 5 V, uma duração de 3 segundos e centrado em t=2 segundos. Este pulso pode ser expresso usando a função retangular, escrita como,

<img alt="Equation1" src="/files/ftp_upload/16041/16041_PT%20EQUATION_1.svg" style="text-align: center; height: 36px;">

A síntese do pulso retangular pode ser demonstrada graficamente adicionando duas funções de degrau deslocadas no tempo sequencialmente. Em termos gerais, uma função retangular unitária sempre pode ser expressa usando a função de degrau unitária da seguinte forma:

<img alt="Equation2" src="/files/ftp_upload/16041/16041_PT%20EQUATION_2.svg" style="text-align: center; height: 36px;">

A função triangular unitária é matematicamente expressa por meio da função triangular. Ela tem altura unitária e é centrada na origem. Por exemplo, considere um pulso triangular centrado em t=3 segundos, com uma magnitude de 2 e uma largura de 2 segundos. Para expressar esse pulso triangular, substitua cada t por t−3 e defina a largura igual a 2. O sinal definido pode ser escrito como,

<img alt="Equation3" src="/files/ftp_upload/16041/16041_PT%20EQUATION_3.svg" style="text-align: center; height: 36px;">

Essa função de pulso triangular pode ser ilustrada graficamente, mostrando como sua altura atinge 2 no centro e diminui para zero nas bordas, abrangendo uma largura total de 2 segundos.

As funções retangulares e triangulares unitárias são fundamentais no processamento de sinais para representar várias formas de onda e são usadas em várias aplicações para modelagem e análise de sinais e sistemas. Essas funções são essenciais para entender comportamentos e operações de sinais mais complexos.

Função de pulso retangular e triangular

A função de pulso retangular unitário é matematicamente representada pela função retangular centrada na origem com uma altura de uma unidade.
Dois...

Education

JoVE Core

Electrical Engineering

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Unit 1

Unidade 1

Introduction to Signals and Systems

Introdução a Sinais e Sistemas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

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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classification of signals

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Signal Symmetry and Decomposition

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basic continuous time signals

Step, Impulse, and Ramp Signals

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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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basic discrete time signals

Discrete-Time Signal Basics and Shapes

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basic operations on signals

Signal Transformations in Time and Amplitude

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classification of systems-i

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Continuous-time and discrete-time systems are two common ways to model signals and their outputs. In continuous-time systems, both input and output signals change smoothly as time moves continuously. These systems are often written with differential or algebraic equations. An RC circuit is one example of a continuous-time system. Its input and output voltage can be related by a differential equation based on Ohm’s law and the capacitor relation. Discrete-time systems work differently. Their...

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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