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

Les opérations de base du signal sont l’inversion temporelle, la mise à l’échelle, le décalage et les transformations d’amplitude.
L'inversion temporelle reflète un signal en temps continu autour de l'axe vertical au moment égal à zéro, obtenu en remplaçant « t » par moins « t ». Pour un signal réfléchi, les résultats sont présentés graphiquement.
L'échelle temporelle compresse ou étend un signal dans le temps en remplaçant « t » par « at », où « a » est constant. Si l’intensité de cette constante est supérieure à 1, le signal est compressé ; S'il est inférieur à 1, il s'étend.
Une valeur négative de cette constante induit à la fois l’inversion temporelle et la compression ou l’expansion. Cela peut être représenté graphiquement à l’aide du signal considéré.
Le décalage temporel d'un signal en temps continu s'effectue en remplaçant « t » par « t − t0' », où « t0' est constant. Une constante positive retarde et décale le signal vers la droite à partir de l’origine, tandis qu’une constante négative avance le signal et le décale vers la gauche.
Les transformations d'amplitude d'un signal en temps continu prennent la forme générale où 'A' et 'B' sont des constantes. Le graphique montre une transformation d’amplitude d’un signal illustré.

opérations de base sur les signaux

Basic Operations on Signals

Les opérations de base sur les signaux comprennent l'inversion temporelle, la mise à l'échelle temporelle, le décalage temporel et les transformations d'amplitude. Ces opérations sont fondamentales dans le traitement et l'analyse du signal.

L'inversion temporelle reflète un signal à temps continu autour de l'axe vertical à t=0. On y parvient en remplaçant t par −t. Par exemple, si l’on considère un signal x(t), le signal inversé dans le temps est x(−t). Cette opération peut être représentée graphiquement, en montrant le signal réfléchi.

<img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="height: 150px;">

La mise à l'échelle temporelle comprime ou étend un signal dans le temps en remplaçant t par at, où a est une constante. Si ∣a∣&gt;1, le signal se comprime; si ∣a∣&lt;1, il se dilate. Une valeur négative de a induit à la fois une inversion du temps et une compression ou une expansion. Une représentation graphique de cette opération sur un signal illustre ces effets.

Le décalage temporel d'un signal à temps continu se fait en remplaçant t par t−t_0, où t_0 est une constante. Un t_0 positif retarde et décale le signal vers la droite, tandis qu'un t_0 négatif avance le signal et le décale vers la gauche. Par exemple, un signal x(t) décalé de t_0 est représenté par x(t−t_0).

Les transformations d'amplitude d'un signal à temps continu sont généralement de la forme Ax(t)+B, où A et B sont des constantes. Ces transformations permettent de mettre l’amplitude à l'échelle et peuvent également la décaler verticalement. Graphiquement, une transformation d'amplitude d'un signal montre l'effet de la mise à l'échelle par A et du décalage par B.

Ces opérations de base (inversion temporelle, mise à l'échelle, décalage et transformations d'amplitude) sont des outils essentiels pour la manipulation et l’analyse des signaux, permettant divers ajustements et modifications dans les applications de traitement du signal.

Opérations de base sur les signaux

Les opérations de base du signal sont l’inversion temporelle, la mise à l’échelle, le décalage et les transformations d’amplitude.
L’inversion temporelle reflète un signal en temps continu autour de la ...

Education

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Electrical Engineering

Génie électrique

Unit 1

Unité 1

Introduction to Signals and Systems

Introduction aux signaux et systèmes

KEY TERMS AND CONCEPTS

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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.

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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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Signal Transformations in Time and Amplitude

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