Name: discrete-time signal basics and shapes
Uploaded: 2024-09-26T13:16:53.000Z
Duration: 1 min 16 s
Channel: JoVE

La séquence d'unités pas est exprimée par 1 pour zéro et les valeurs positives de l'entier 'n'. Cela peut être affiché graphiquement à l’aide d’un ensemble de huit points d’échantillonnage.
L’impulsion unitaire ou la séquence d’échantillon est exprimée mathématiquement pour toutes les valeurs discrètes de n. C'est zéro pour toutes les valeurs 'n' sauf à zéro.
L’impulsion unitaire est la première différence du pas unitaire, tandis que le pas unitaire est la somme cumulative de l’échantillon unitaire. Cette corrélation est démontrée visuellement à l’aide d’un graphique.
La séquence d’impulsions unitaires peut échantillonner efficacement la valeur du signal à n égale à zéro puisqu’elle n’est non nulle qu’en ce point.
La séquence de rampe d’unités présente une escalade linéaire de la valeur avec l’augmentation du nombre d’échantillons. Pour une séquence de 12 échantillons sur une rampe unitaire, le graphique montre une augmentation linéaire de l’amplitude avec le numéro d’échantillon.
Une séquence sinusoïdale est définie par ses paramètres d’amplitude et de phase.
La suite exponentielle est définie à l’aide de nombres complexes, avec des séquences décroissantes et croissantes exponentiellement représentées sur un graphique.

signaux de base à temps discret

Basic Discrete Time Signals

La séquence échelon unité est définie comme 1 pour les valeurs nulles et positives de l'entier n. Cette séquence peut être représentée graphiquement à l'aide d'un ensemble de huit points d'échantillonnage, montrant une fonction en escalier commençant à n = 0 et restant constante par la suite.

L'impulsion unitaire ou la séquence d'échantillons est exprimée mathématiquement comme étant nulle pour toutes les valeurs de n, sauf à n = 0, où elle est égale à un. La séquence d'impulsion unitaire, désignée par δ(n), est la première différence de la séquence échelon unité, tandis que la séquence échelon unité u(n) est la somme cumulative de la séquence d'impulsion unitaire. Cette relation peut être démontrée visuellement à l'aide d'un graphique, mettant en évidence la manière dont l'impulsion unitaire peut échantillonner efficacement la valeur du signal à n = 0.

La séquence de rampe unitaire présente une augmentation linéaire de la valeur avec l'augmentation du nombre d'échantillons. Par exemple, une séquence de 12 échantillons sur une rampe unitaire affichera une augmentation linéaire de l'amplitude avec chaque numéro d'échantillon, représentée graphiquement par une ligne droite.

Une séquence sinusoïdale est définie par ses paramètres d'amplitude et de phase. Cette séquence peut être représentée comme suit :

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_1.svg" style="height: 14px;">

où A est l'amplitude, ω est la fréquence angulaire et Φ est la phase.

La séquence exponentielle est définie à l'aide de nombres complexes, avec des séquences exponentielles décroissantes et croissantes représentées sur un graphique. Une séquence décroissant de manière exponentielle peut être écrite comme suit :

<img alt="Equation2" src="/files/ftp_upload/16043/16043_PT%20EQUATION_2.svg" style="height: 14px;">

tandis qu'une séquence croissant de manière exponentielle est exprimée comme suit :

<img alt="Equation3" src="/files/ftp_upload/16043/16043_PT%20EQUATION_3.svg" style="height: 14px;">

où A est l'amplitude initiale et α est une constante positive. Ces séquences sont fondamentales dans l’analyse de diverses applications de traitement du signal en raison de leurs propriétés et comportements uniques.

Signaux de base à temps discret

La séquence d'unités pas est exprimée par 1 pour zéro et les valeurs positives de l'entier 'n'. Cela peut être affiché graphiquement à l’aide d’un ensemble de huit ...

Education

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JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Introduction to Signals and Systems

Introduction aux signaux et systèmes

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

discrete-time signal basics and shapes

Discrete-time signals include several basic sequences used in signal processing. The unit step sequence is 1 for zero and positive values of the integer n. A graph of eight sample points shows it as a step that begins at n = 0 and stays constant after that.

The unit impulse, also called the sample sequence, is 0 for every n except at n = 0, where it equals 1. This sequence is written as δ(n). It is the first difference of the unit step sequence, and the unit step sequence u(n) is the cumulative sum of the unit impulse sequence. A graph can show how the impulse samples the signal value at n = 0.

The unit ramp sequence increases linearly as the sample number increases. For example, a 12-sample ramp rises by the same amount at each sample, so its graph appears as a straight line. This makes the ramp easy to recognize on a plot.

A sinusoidal sequence is set by its amplitude and phase. In the expression for this sequence, A is the amplitude, ω is the angular frequency, and Φ is the phase. An exponential sequence uses complex numbers. It can describe both exponentially decaying and exponentially increasing sequences. The decaying form and the increasing form are both shown on graphs, with A as the initial amplitude and α as a positive constant. These basic sequences are important because they help describe many signal-processing applications.

Discrete-Time Signal Basics and Shapes

signal and system

Signals and Systems in Everyday Data

Signals and systems help describe how data moves through the world. A signal x(t) is a set of data or a time function that represents a variable of interest. It can carry information about atmospheric temperature, humidity, human voice, television images, a dog’s bark, or birdsongs. A signal can also depend on more than one independent variable. An image, for example, depends on horizontal and vertical position, so it can be treated as a two-dimensional signal. In this course, the focus is on...

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Signals in signal processing are grouped by time behavior, amplitude, and whether they start before or after time zero. These signal classes help students describe and compare signals before they are analyzed or processed. A continuous-time signal has a value at every instant in time. A discrete-time signal has values only at specific moments, often written as x(n), where n is an integer. Discrete-time signals often come from systems with naturally discrete values, such as digital audio...

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Step, Impulse, and Ramp Signals

Step, impulse, and ramp signals are the main basic continuous-time signals. They are also called singularity functions. These signals are known for discontinuities or for derivatives that are discontinuous. The unit step function, written as u(t), is zero for negative time values and one for positive time values. It has a jump at t = 0. In many cases, it can model an abrupt change, such as the step voltage that appears when a car ignition key is turned. The derivative of the unit step...

rectangular and triangular pulse function

rectangular-and-triangular-pulse-function

Modeling Pulses with Rectangles and Triangles

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exponential and sinusoidal signals

Complex Exponentials in Signal Behavior

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basic discrete time signals

Discrete-time signals include several basic sequences used in signal processing. The unit step sequence is 1 for zero and positive values of the integer n. A graph of eight sample points shows it as a step that begins at n = 0 and stays constant after that. The unit impulse, also called the sample sequence, is 0 for every n except at n = 0, where it equals 1. This sequence is written as δ(n). It is the first difference of the unit step sequence, and the unit step sequence u(n) is the...

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key terms and concepts

Learn the key discrete-time signal shapes used in signal processing, including the unit step, impulse, ramp, sinusoidal, and exponential sequences.

Discrete-Time Signal Basics and Shapes | 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

Discrete-Time Signal Basics and Shapes

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