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

La linéarité est une propriété du système avec une relation directe d’entrée-sortie, combinant homogénéité et additivité.
L’homogénéité dicte que si une entrée est multipliée par une constante, la sortie est multipliée par la même constante. L'additivité signifie que la réponse à plusieurs entrées est la somme de leurs réponses individuelles.
Un système qui a à la fois des propriétés d’homogénéité et d’additivité est classé comme un système linéaire.
Les systèmes linéaires comprennent des circuits avec des résistances, des condensateurs et des inductances qui adhèrent au principe de superposition.
À l’inverse, les systèmes qui ne respectent pas l’équation de linéarité sont classés comme non linéaires, y compris souvent des dispositifs tels que des redresseurs et des diodes.
Un système causal est caractérisé par une réponse actuelle indépendante des valeurs d’entrée futures. Un exemple peut être le mouvement d'une voiture, qui ne peut pas prédire les actions de conduite futures.
Les systèmes non causaux, tels que les filtres idéaux, ne peuvent pas être physiquement réalisés et ne suivent pas le principe de causalité.
Les systèmes dynamiques montrent la mémoire, où la sortie est affectée à la fois par les entrées passées et futures.
Les systèmes statiques sont des systèmes sans mémoire ou instantanés où la sortie de courant est uniquement basée sur l’entrée actuelle.

classification des systèmes - i

La linéarité est une propriété d'un système caractérisée par une relation entrée-sortie directe, combinant homogénéité et additivité.

L'homogénéité stipule que si une entrée x(t) est multipliée par une constante c, la sortie y(t) est multipliée par la même constante. Mathématiquement, cela s'exprime comme suit :
<img alt="Equation1" src="/files/ftp_upload/16045/16045_PT%20EQUATION_1.svg" style="height: 14px;">

L'additivité signifie que la réponse à la somme de plusieurs entrées est la somme de leurs réponses individuelles. Pour les entrées x_1(t) et x_2(t) produisant respectivement les sorties y_1(t) et y_2(t) :
<img alt="Equation2" src="/files/ftp_upload/16045/16045_PT%20EQUATION_2.svg" style="height: 14px;">

La combinaison de l'homogénéité et de l'additivité donne l'équation d'un système linéaire :
<img alt="Equation3" src="/files/ftp_upload/16045/16045_PT%20EQUATION_3.svg" style="height: 14px;">

Les systèmes linéaires comprennent les circuits avec des résistances, des condensateurs et des inductances qui respectent le principe de superposition. À l'inverse, les systèmes qui n’obéissent pas à l'équation de linéarité sont classés comme non linéaires, tels que les redresseurs et les diodes.

Un système causal est un système dans lequel la réponse actuelle est indépendante des valeurs d'entrée futures. Par exemple, le mouvement d'une voiture ne peut pas prédire les actions de conduite futures, ce qui en fait un système causal. En revanche, les systèmes non causaux comme les filtres idéaux ne peuvent pas être matérialisés physiquement car ils ne suivent pas le principe de causalité.

Les systèmes dynamiques sont dotés d'une mémoire, c'est-à-dire que la sortie dépend des entrées passées et présentes. Un exemple est un circuit électrique avec des condensateurs ou des inducteurs, où la sortie actuelle est influencée par les entrées passées. Les systèmes statiques, également connus sous le nom de systèmes sans mémoire ou instantanés, ont des sorties uniquement basées sur l'entrée actuelle, comme un simple circuit de résistance où la tension de sortie est une fonction directe de la tension d'entrée actuelle.

La compréhension de ces propriétés (linéarité, causalité et mémoire) est essentielle pour analyser et concevoir des systèmes dans divers domaines de l'ingénierie.

Classification des systèmes - I

La linéarité est une propriété du système avec une relation directe d’entrée-sortie, combinant homogénéité et additivité.
L’homogénéité dicte que si une entrée est ...

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Electrical Engineering

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Unit 1

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Introduction to Signals and Systems

Introduction aux signaux et systèmes

KEY TERMS AND CONCEPTS

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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

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Complex Exponentials in Signal Behavior

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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.

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System Properties: Linearity, Causality, Memory

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