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

La linealidad es una propiedad del sistema con una relación directa de entrada-salida, que combina homogeneidad y aditividad.
La homogeneidad dicta que si una entrada se multiplica por una constante, la salida se multiplica por la misma constante. La aditividad significa que la respuesta a múltiples entradas es la suma de sus respuestas individuales.
Un sistema que tiene propiedades de homogeneidad y aditividad se clasifica como un sistema lineal.
Los sistemas lineales incluyen circuitos con resistencias, condensadores e inductores que se adhieren al principio de superposición.
Por el contrario, los sistemas que no obedecen la ecuación de linealidad se clasifican como no lineales, a menudo incluyendo dispositivos como rectificadores y diodos.
Un sistema causal se caracteriza por una respuesta actual independiente de los valores de entrada futuros. Un ejemplo puede ser el movimiento de un automóvil, que no puede predecir futuras acciones de conducción.
Los sistemas no causales, como los filtros ideales, no pueden realizarse físicamente y no siguen el principio de causalidad.
Los sistemas dinámicos muestran memoria, donde la salida se ve afectada por entradas pasadas y futuras.
Los sistemas estáticos son sistemas instantáneos o sin memoria en los que la salida de corriente se basa únicamente en la entrada presente.

clasificación de sistemas-i

La linealidad es una propiedad del sistema que se caracteriza por una relación directa de entrada-salida, que combina homogeneidad y aditividad.
La homogeneidad dicta que si una entrada x(t) se multiplica por una constante c, la salida y(t) se multiplica por la misma constante. Matemáticamente, esto se expresa como: 
<img alt="Equation1" src="/files/ftp_upload/16045/16045_PT%20EQUATION_1.svg" style="text-align: center; height: 14px;">
La aditividad significa que la respuesta a la suma de múltiples entradas es la suma de sus respuestas individuales. Para las entradas x_1(t) y x_2(t) que producen salidas y_1(t) y y_2(t), respectivamente: 
<img alt="Equation2" src="/files/ftp_upload/16045/16045_PT%20EQUATION_2.svg" style="text-align: center; height: 14px;">
Al combinar la homogeneidad y la aditividad se obtiene la ecuación de un sistema lineal: 
<img alt="Equation3" src="/files/ftp_upload/16045/16045_PT%20EQUATION_3.svg" style="text-align: center; height: 14px;">
Los sistemas lineales incluyen circuitos con resistencias, condensadores e inductores que se adhieren al principio de superposición. Por el contrario, los sistemas que no obedecen la ecuación de linealidad se clasifican como no lineales, como los rectificadores y los diodos.
Un sistema causal es aquel en el que la respuesta actual es independiente de los valores de entrada futuros. Por ejemplo, el movimiento de un automóvil no puede predecir las acciones de conducción futuras, lo que lo convierte en un sistema causal. Por el contrario, los sistemas no causales, como los filtros ideales, no se pueden realizar físicamente porque no siguen el principio de causalidad. 
Los sistemas dinámicos presentan memoria, donde la salida depende de las entradas pasadas y presentes. Un ejemplo es un circuito eléctrico con capacitores o inductores, donde la salida actual está influenciada por las entradas pasadas. Los sistemas estáticos, también conocidos como sistemas sin memoria o instantáneos, tienen salidas basadas únicamente en la entrada actual, como un circuito simple con resistencias donde la tensión de salida es una función directa de la tensión de entrada actual.
Comprender estas propiedades (linealidad, causalidad y memoria) es esencial para analizar y diseñar sistemas en varios campos de la ingeniería.

Clasificación de sistemas-I

La linealidad es una propiedad del sistema con una relación directa de entrada-salida, que combina homogeneidad y aditividad.
La homogeneidad dicta que si una entrada es ...

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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

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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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System Properties: Linearity, Causality, Memory

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