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

单位阶跃序列在整数“n”为零或正值时取值为1。该序列可通过一组八个采样点进行图形化表示。
单位脉冲或采样序列在数学上表示为所有离散值 n 的函数。当 n 取所有非零值时，其值为零。n除零以外的所有值。
单位脉冲是单位阶跃的一阶差分，而单位阶跃是单位样本的累积和。这一关联关系通过图形直观地展示出来。
单位脉冲序列能够有效采样 n 等于零时的信号值，因为它仅在该点处非零。
单位斜坡序列随着样本数量的增加呈现出线性增长的趋势。对于包含12个样本的单位斜坡序列，该图显示其幅值随样本数量呈线性增加。
正弦序列由其振幅和相位参数定义。
指数序列使用复数定义，其指数衰减和指数增长序列在图中表示。

基本离散时间信号

Basic Discrete Time Signals

对于零和正整数 n 来说，可以将单位阶跃序列定义为 1。该序列可以通过使用一组八个采样点以图形的形式来进行表示，同时将其表示为从 n=0 开始的阶跃函数，并在随后保持不变。

在数学中，可以将单位脉冲或样本序列的所有 n 值均表示为零，只有 n=0 时为 1。单位脉冲序列可以用 δ(n) 来进行表示，这是单位阶跃序列的一阶差分，而单位阶跃序列 u(n) 则是单位脉冲序列的累积和。这种关系可以通过图表来将其直观地进行表示，这突出了单位脉冲在 n=0 时是如何对信号值进行有效采样。

单位斜坡序列的值会随着样本数量的增加而线性增加。例如，单位斜坡上的 12 个样本序列将会随着每个样本数量的增加而表现出幅度的线性增加，并在图形上表示为一条直线。

正弦序列是由其振幅和相位参数来进行定义的。可以将该序列表示为：

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_1.svg" style="height: 14px;">

其中，A 是振幅，ω 是角频率，φ 是相位。

指数序列是用复数来进行定义的，并在图形上将其表示为指数衰减和递增序列。指数衰减序列可以表示为：

<img alt="Equation2" src="/files/ftp_upload/16043/16043_PT%20EQUATION_2.svg" style="height: 14px;">

而指数递增序列可以表示为：

<img alt="Equation3" src="/files/ftp_upload/16043/16043_PT%20EQUATION_3.svg" style="height: 14px;">

其中，A 是初始振幅，α 是正常数。这些序列具有独特的属性和行为，从而使其能够成为分析各种信号处理应用场景的基础。

单位阶跃序列在整数 'n' 的零值和正值时表达为 1。这可以通过一组八个……以图形方式显示。

Education

教育

JoVE Core

Electrical Engineering

电气工程

Unit 1

第一单元

Introduction to Signals and Systems

信号与系统导论

KEY TERMS AND CONCEPTS

关键术语与概念

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

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Signal Types by Time and Amplitude

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Power and Energy in Electrical Signals

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Signal Symmetry and Decomposition

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basic continuous time signals

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

Rectangular and triangular pulse functions are basic signal shapes used to model waveforms in signal processing. The rectangular pulse has a flat top and is centered at the origin with a height of one unit. It is described by two parameters: T, which gives the center location on the time axis, and τ, which sets the pulse duration. A rectangular pulse can also represent a real signal with a chosen amplitude and length. For example, a pulse with a 5 V amplitude, a 3-second duration, and a center...

exponential and sinusoidal signals

Complex Exponentials in Signal Behavior

Exponential and sinusoidal signals are used to describe how waveforms change over time. The continuous-time exponential function uses constants α and A. When both are real, it shows exponential growth or decay. Graphs of these signals make the rise or drop easy to see. When α is purely imaginary, the signal becomes a complex exponential. In this form, j is the imaginary unit and ω0 is the angular frequency. A complex exponential is periodic when its magnitude is unity. That periodic behavior...

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...

basic operations on signals

Signal Transformations in Time and Amplitude

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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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