Name: continuous and discrete system models
Uploaded: 2024-09-26T13:16:54.000Z
Duration: 1 min 31 s
Channel: JoVE

Os sistemas de tempo contínuo têm sinais de entrada e saída contínuos, com o tempo medido continuamente, e geralmente são definidos por equações diferenciais ou algébricas.
Por exemplo, em um circuito RC, a relação entre a tensão de entrada e saída é expressa por meio de uma equação diferencial derivada usando a lei de Ohm e a relação tensão-corrente do capacitor.
Os sistemas de tempo discreto processam sinais de entrada e saída em intervalos específicos e seu comportamento é descrito por equações de diferença em instâncias de tempo distintas. Um exemplo de tal sistema é um modelo simples para o saldo em uma conta bancária mês a mês.
Outro tipo de sistema é variável no tempo e invariante no tempo.
Um sistema variável no tempo tem parâmetros que mudam com o tempo. Os sistemas de tempo contínuo e variáveis no tempo são descritos por equações diferenciais com coeficientes dependentes do tempo, enquanto os sistemas de tempo discreto e variáveis no tempo são descritos por equações de diferença com parâmetros dependentes do tempo.
Os sistemas invariantes no tempo produzem uma saída que, quando o sinal de entrada é deslocado no tempo, muda de forma idêntica sem alterar as características do sistema.
Um circuito RC é invariante no tempo se os valores de resistência e capacitância permanecerem constantes. Se eles flutuarem, o sistema se tornará uma variante de tempo, pois os resultados do experimento variam dependendo de quando o experimento é conduzido.

classificação de sistemas-ii

Sistemas de tempo contínuo têm sinais de entrada e saída contínuos, com tempo medido continuamente. Esses sistemas são geralmente definidos por equações diferenciais ou algébricas. Por exemplo, em um circuito RC, a relação entre tensão de entrada e saída é expressa por meio de uma equação diferencial derivada da lei de Ohm e da relação do capacitor,
<img alt="Equation1" src="/files/ftp_upload/16046/16046_PT%20EQUATION_1.svg" style=" height: 30px;">
Sistemas de tempo discreto têm sinais de entrada e saída em intervalos específicos, definidos em instantes distintos por equações de diferença. Um exemplo é um modelo simples para o saldo em uma conta bancária de mês a mês, representado como,
<img alt="Equation2" src="/files/ftp_upload/16046/16046_PT%20EQUATION_2.svg" style=" height: 14px;">
onde B[n] é o saldo no mês n, D[n] é o depósito e W[n] é o saque.
Os sistemas também podem ser categorizados como variáveis ​​no tempo ou invariantes no tempo. Um sistema que varia no tempo tem parâmetros que mudam ao longo do tempo. Sistemas que variam no tempo contínuos são descritos por equações diferenciais que variam no tempo, enquanto sistemas que variam no tempo discretos são definidos por equações de diferença que variam no tempo.
Um sistema invariante no tempo exibe mudanças de tempo idênticas em sinais de saída quando o sinal de entrada é deslocado no tempo. Matematicamente, se y(t) é a saída para a entrada x(t), então para um sistema invariante no tempo, y(t−t_0) é a saída para a entrada x(t−t_0). Por exemplo, um circuito RC é invariante no tempo se os valores de resistência R e capacitância C permanecerem constantes. Se esses valores flutuarem, o sistema se torna variante no tempo, o que significa que os resultados irão variar dependendo de quando o experimento for conduzido.
Entender essas distinções em sistemas de tempo contínuo e discreto, bem como em sistemas variáveis ​​e invariantes no tempo, é crucial para analisar e projetar uma ampla gama de sistemas de engenharia.

Classificação de Sistemas-II

Os sistemas de tempo contínuo têm sinais de entrada e saída contínuos, com o tempo medido continuamente, e são geralmente definidos por diferenciais ou algébricos.

Education

JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

Introduction to Signals and Systems

Introdução a Sinais e Sistemas

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

Classification of Systems-II

continuous and discrete system models

Continuous-time and discrete-time systems are two common ways to model signals and their outputs. In continuous-time systems, both input and output signals change smoothly as time moves continuously. These systems are often written with differential or algebraic equations.

An RC circuit is one example of a continuous-time system. Its input and output voltage can be related by a differential equation based on Ohm’s law and the capacitor relation. Discrete-time systems work differently. Their inputs and outputs are defined at specific time steps, and they are described by difference equations.

A bank account balance from month to month is a simple discrete-time model. In that example, B[n] is the balance at month n, D[n] is the deposit, and W[n] is the withdrawal. Systems are also grouped as time-varying or time-invariant. A time-varying system has parameters that change with time, while a time-invariant system keeps the same shift in output when the input is shifted.

For a time-invariant system, if y(t) is the output for input x(t), then y(t − t0) is the output for x(t − t0). An RC circuit is time-invariant when the resistance R and capacitance C stay constant. If those values change, the system becomes time-variant. Then the result depends on when the experiment is done. Knowing these categories helps in analyzing and designing many engineering systems.

Continuous and Discrete System Models

signal and system

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classification of signals

Signal Types by Time and Amplitude

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...

energy and power signals

Power and Energy in Electrical Signals

Power and energy in electrical signals are measured from voltage and current across a resistor. These signals help describe how much energy a signal carries and how much power it delivers over time. For a continuous-time signal, total energy is found by integrating the square of the signal's magnitude over a chosen time interval. Time-averaged power is then the total energy divided by the length of that interval. For a discrete-time signal, total energy is found by summing the squares of the...

even and odd signals

Signal Symmetry and Decomposition

Signal symmetry helps classify continuous-time and discrete-time signals as even or odd. An even signal matches its time-reversed version. It mirrors around the vertical axis, so the values at negative time match the values at positive time. An odd signal does not match its time-reversed counterpart. It has antisymmetry about the vertical axis. These symmetry rules are used in both continuous-time and discrete-time signal analysis. Any continuous-time signal can be split into even and odd...

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 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...

basic operations on signals

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...

classification of systems-i

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...

classification of systems-ii

Continuous-time and discrete-time systems are two common ways to model signals and their outputs. In continuous-time systems, both input and output signals change smoothly as time moves continuously. These systems are often written with differential or algebraic equations. An RC circuit is one example of a continuous-time system. Its input and output voltage can be related by a differential equation based on Ohm’s law and the capacitor relation. Discrete-time systems work differently. Their...

key terms and concepts

Learn how continuous-time and discrete-time systems differ, plus how time-varying and time-invariant behavior is identified using RC circuits and bank account examples.

Continuous and Discrete System Models | 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

Continuous and Discrete System Models

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