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

线性是一种系统特性，具有直接的输入-输出关系，结合了齐次性和可加性。
齐次性要求输入乘以一个常数时，输出也乘以相同的常数。可加性意味着系统对多个输入的响应等于各个输入单独作用时响应的总和。
同时具有齐次性和可加性性质的系统被归类为线性系统。
线性系统包括包含电阻、电容和电感的电路，这些电路遵循叠加原理。
相反，不满足线性方程的系统被归类为非线性系统，通常包括整流器和二极管等器件。
因果系统的特点是其当前响应不依赖于未来的输入值。例如，汽车的运动无法预测未来的驾驶操作。
非因果系统（如理想滤波器）无法物理实现，且不遵循因果性原则。
动态系统具有记忆性，其输出受过去和未来输入的共同影响。
静态系统是无记忆系统或瞬时系统，其当前输出仅取决于当前输入。

系统分类-i

Classification of Systems-I

线性是一种系统属性，其中的特征是直接的输入-输出关系，并且还结合了同质性和可加性。

同质性规定，如果输入 x(t) 乘以常数 c，则会输出 y(t) 乘以相同的常数。在数学中，可以将其表示为：

<img alt="Equation1" src="/files/ftp_upload/16045/16045_PT%20EQUATION_1.svg" style="height: 14px;">

可加性指的是由多个输入所组成的响应是它们各自的响应之和。对于输入 x_1(t) 和 x_2(t)，则会分别产生输出 y_1(t) 和 y_2(t)：

<img alt="Equation2" src="/files/ftp_upload/16045/16045_PT%20EQUATION_2.svg" style="height: 14px;">

将同质性和可加性进行结合，便能够得到线性系统方程：

<img alt="Equation3" src="/files/ftp_upload/16045/16045_PT%20EQUATION_3.svg" style="height: 14px;">

线性系统包括遵循叠加原理的电阻器、电容器和电感器电路。相反，不遵循线性方程的系统则会被归类为非线性系统，例如整流器和二极管。

因果系统指的当前响应与未来输入值无关的系统。例如，汽车的运动无法预测未来的驾驶行为，因此它是一个因果系统。相反，像理想滤波器这样的非因果系统则无法在物理上实现，因为它们不遵循因果关系原理。

动态系统具有记忆性，其输出取决于过去和现在的输入。例如，假设有一个带有电容器或电感器的电路，其当前输出会受到过去输入所产生的影响。静态系统（也称为无记忆或瞬时系统）的输出会完全基于当前的输入，例如简单的电阻电路，其输出电压是当前输入电压的直接函数。

了解这些属性（线性、因果关系和记忆性）对于分析和设计各个工程领域的系统来说是至关重要的。

系统分类-I

线性是一种系统特性，具有直接的输入-输出关系，包含齐次性和可加性。  
齐次性要求，如果输入被……

Education

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JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Introduction to Signals and Systems

信号与系统导论

KEY TERMS AND CONCEPTS

关键术语与概念

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

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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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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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