Name: signal transformations in time and amplitude
Uploaded: 2024-09-26T13:16:54.000Z
Duration: 1 min 22 s
Channel: JoVE

Las operaciones básicas de señal son la inversión de tiempo, el escalado, el desplazamiento y las transformaciones de amplitud.
La inversión del tiempo refleja una señal de tiempo continuo sobre el eje vertical en un tiempo igual a cero, que se logra sustituyendo 't' por menos 't'. Para una señal considerada, los resultados se muestran gráficamente.
El escalado de tiempo comprime o expande una señal en el tiempo reemplazando 't' por 'at', donde 'a' es constante. Si la magnitud de esta constante es mayor que 1, la señal se comprime; si es menor que 1, se expande.
Un valor negativo de esta constante induce tanto la inversión del tiempo como la compresión o expansión. Esto se puede representar gráficamente utilizando la señal considerada.
El desplazamiento en el tiempo de una señal de tiempo continuo se realiza reemplazando 't' por 't − t0', donde 't0' es constante. Una constante positiva retrasa y desplaza la señal a la derecha desde el origen, mientras que una negativa hace avanzar la señal y la desplaza a la izquierda.
Las transformaciones de amplitud de una señal de tiempo continuo toman la forma general donde 'A' y 'B' son constantes. El gráfico muestra una transformación de amplitud de una señal ejemplificada.

operaciones básicas en señales

Basic Operations on Signals

Las operaciones básicas en señales incluyen inversión temporal, escalado en el tiempo, desplazamiento de tiempo y transformaciones de amplitud. Estas operaciones son fundamentales en el procesamiento y análisis de señales.


La inversión temporal refleja una señal de tiempo continuo sobre el eje vertical en t=0. Esto se logra sustituyendo t por −t. Por ejemplo, si se considera una señal x(t), la señal invertida en el tiempo es x(−t). Esta operación se puede representar gráficamente, mostrando la señal reflejada.


<img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="height: 150px;">

El escalado en el tiempo comprime o expande una señal en el tiempo reemplazando t por at, donde a es una constante. Si ∣a∣&gt;1, la señal se comprime; Si ∣a∣&lt;1, se expande. Un valor negativo de a induce tanto inversión temporal como compresión o expansión. Una representación gráfica de esta operación en una señal demuestra estos efectos.


El desplazamiento temporal de una señal de tiempo continuo se realiza reemplazando t por t−t_0, donde t_0 es una constante. Un t_0 positivo retrasa y desplaza la señal hacia la derecha, mientras que un t_0 negativo avanza la señal y la desplaza hacia la izquierda. Por ejemplo, una señal x(t) desplazada por t_0 se representa como x(t−t_0).


Las transformaciones de amplitud de una señal de tiempo continuo generalmente tienen la forma Ax(t)+B, donde A y B son constantes. Estas transformaciones escalan la amplitud y también pueden desplazarla verticalmente. Gráficamente, una transformación de amplitud de una señal muestra el efecto de escalar en A y desplazar en B.


Estas operaciones básicas (inversión temporal, escalado, desplazamiento y transformaciones de amplitud) son herramientas esenciales para manipular y analizar señales, lo que permite realizar diversos ajustes y modificaciones en aplicaciones de procesamiento de señales.

Operaciones básicas en señales

Las operaciones básicas de señal son la inversión de tiempo, el escalado, el desplazamiento y las transformaciones de amplitud.
La inversión del tiempo refleja una señal de tiempo continuo ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Introduction to Signals and Systems

Introducción a Señales y Sistemas

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

signal transformations in time and amplitude

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized.

Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly.

Time scaling changes how fast or slow a signal appears in time by replacing t with at, where a is a constant. If |a| &gt; 1, the signal compresses. If |a| &lt; 1, the signal expands. A negative value of a causes time reversal as well as compression or expansion.

Time shifting moves a continuous-time signal left or right by replacing t with t - t0, where t0 is a constant. A positive t0 delays the signal and shifts it to the right. A negative t0 advances the signal and shifts it to the left. Amplitude transformations use the form Ax(t) + B, where A and B are constants. These changes scale the signal’s height and can shift it up or down vertically.

Signal Transformations in Time and Amplitude

signal-transformations-in-time-and-amplitude

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Complex Exponentials in Signal Behavior

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basic discrete time signals

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basic operations on signals

Signal transformations in time and amplitude are key tools in signal processing. They include time reversal, time scaling, time shifting, and amplitude changes. These operations help students describe how a continuous-time signal changes when it is mirrored, stretched, moved, or resized. Time reversal flips a continuous-time signal about the vertical axis at t = 0. It is done by replacing t with -t, so x(t) becomes x(-t). A graph of the signal shows this mirrored shape clearly. Time scaling...

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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

Signal Transformations in Time and Amplitude

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