Name: system properties: linearity, causality, memory
Uploaded: 2024-09-26T13:16:54.000Z
Duration: 1 min 26 s
Channel: JoVE

A linearidade é uma propriedade do sistema com uma relação direta de entrada-saída, combinando homogeneidade e aditividade.
A homogeneidade determina que, se uma entrada é multiplicada por uma constante, a saída é multiplicada pela mesma constante. Aditividade significa que a resposta a várias entradas é a soma de suas respostas individuais.
Um sistema que possui propriedades de homogeneidade e aditividade é classificado como um sistema linear.
Os sistemas lineares incluem circuitos com resistores, capacitores e indutores que aderem ao princípio da superposição.
Por outro lado, os sistemas que não obedecem à equação de linearidade são classificados como não lineares, muitas vezes incluindo dispositivos como retificadores e diodos.
Um sistema causal é caracterizado por uma resposta atual independente de valores de entrada futuros. Um exemplo pode ser o movimento de um carro, que não pode prever ações futuras de direção.
Sistemas não causais, como filtros ideais, não podem ser realizados fisicamente e não seguem o princípio da causalidade.
Os sistemas dinâmicos mostram memória, onde a saída é afetada por entradas passadas e futuras.
Os sistemas estáticos são sistemas sem memória ou instantâneos em que a saída de corrente é baseada exclusivamente na entrada atual.

classificação de sistemas-i

Linearidade é uma propriedade do sistema caracterizada por uma relação direta de entrada-saída, combinando homogeneidade e aditividade.
Homogeneidade determina que se uma entrada x(t) for multiplicada por uma constante c, a saída y(t) será multiplicada pela mesma constante. Matematicamente, isso é expresso como: 
<img alt="Equation1" src="/files/ftp_upload/16045/16045_PT%20EQUATION_1.svg" style="height: 14px;">
Aditividade significa que a resposta à soma de múltiplas entradas é a soma de suas respostas individuais. Para entradas x_1(t) e x_2(t) produzindo saídas y_1(t) e y_2(t), respectivamente:
<img alt="Equation2" src="/files/ftp_upload/16045/16045_PT%20EQUATION_2.svg" style="height: 14px;">
A combinação de homogeneidade e aditividade produz a equação de um sistema linear:
<img alt="Equation3" src="/files/ftp_upload/16045/16045_PT%20EQUATION_3.svg" style="height: 14px;">
Sistemas lineares incluem circuitos com resistores, capacitores e indutores que aderem ao princípio da superposição. Por outro lado, sistemas que não obedecem à equação de linearidade são classificados como não lineares, como retificadores e diodos.
Um sistema causal é aquele em que a resposta atual é independente de valores de entrada futuros. Por exemplo, o movimento de um carro não pode prever ações futuras de direção, tornando-o um sistema causal. Em contraste, sistemas não causais como filtros ideais não podem ser fisicamente realizados, pois não seguem o princípio da causalidade.
Sistemas dinâmicos exibem memória, onde a saída depende de entradas passadas e presentes. Um exemplo é um circuito elétrico com capacitores ou indutores, onde a saída presente é influenciada por entradas passadas. Sistemas estáticos, também conhecidos como sistemas sem memória ou instantâneos, têm saídas baseadas unicamente na entrada presente, como um circuito resistor simples onde a tensão de saída é uma função direta da tensão de entrada atual.
Entender essas propriedades — linearidade, causalidade e memória — é essencial para analisar e projetar sistemas em vários campos da engenharia.

Classificação de Sistemas-I

A linearidade é uma propriedade do sistema com uma relação direta de entrada-saída, combinando homogeneidade e aditividade.
A homogeneidade determina que, se uma entrada for ...

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Introduction to Signals and Systems

Introdução a Sinais e Sistemas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Classification of Systems-I

system properties: linearity, causality, memory

System properties such as linearity, causality, and memory help describe how a system responds to input. These ideas are useful for studying and designing systems in engineering. A system can be checked by looking at how its output changes with different inputs.

Linearity means the input-output relationship follows homogeneity and additivity. Homogeneity says that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Additivity means the response to a sum of inputs equals the sum of the separate responses. Together, these rules define a linear system, and circuits with resistors, capacitors, and inductors can follow the superposition principle.

Systems that do not satisfy the linearity equation are non-linear. Diodes and rectifiers are examples of non-linear systems. Causality is another key property. A causal system depends only on the present input and past inputs, not on future values.

A car’s motion is a simple example of a causal system, because it cannot depend on future driving actions. Non-causal systems, such as ideal filters, are not physically realizable because they do not follow causality. Memory is the last major property. Dynamic systems have memory, so their output depends on past and present inputs, as in circuits with capacitors or inductors. Static systems, also called memoryless or instantaneous systems, depend only on the present input. A simple resistor circuit is an example, since its output voltage is a direct function of the current input voltage.

System Properties: Linearity, Causality, Memory

system-properties-linearity-causality-memory

signal and system

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classification of systems-i

System properties such as linearity, causality, and memory help describe how a system responds to input. These ideas are useful for studying and designing systems in engineering. A system can be checked by looking at how its output changes with different inputs. Linearity means the input-output relationship follows homogeneity and additivity. Homogeneity says that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Additivity means the response...

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key terms and concepts

Explore linearity, causality, and memory in system behavior. Learn how linear, non-linear, causal, dynamic, and static systems differ in engineering.

System Properties: Linearity, Causality, Memory | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

electrical engineering

System Properties: Linearity, Causality, Memory

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