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

연속 시간 시스템은 연속적으로 측정 된 시간과 함께 연속적인 입력 및 출력 신호를 가지며 일반적으로 미분 또는 대수 방정식으로 정의됩니다.
예를 들어, RC 회로에서 입력 전압과 출력 전압 간의 관계는 옴의 법칙과 커패시터의 전압-전류 관계를 사용하여 파생된 차동 방정식을 통해 표현됩니다.
이산시간 시스템은 입력 신호와 출력 신호를 특정 간격으로 처리하며, 그 동작은 서로 다른 시간 인스턴스에서 차분 방정식으로 설명됩니다. 이러한 시스템의 예로는 월별 은행 계좌 잔액에 대한 간단한 모델이 있습니다.
또 다른 유형의 시스템은 시변 및 시변입니다.
시변 시스템에는 시간이 지남에 따라 변경되는 매개변수가 있습니다. 연속시간, 시변 시스템은 시간 종속 계수가 있는 미분 방정식으로 설명되는 반면, 이산 시간, 시변 시스템은 시간 종속 매개변수가 있는 차분 방정식으로 설명됩니다.
시불변 시스템은 입력 신호가 시간 시프팅될 때 시스템의 특성을 변경하지 않고 동일하게 이동하는 출력을 생성합니다.
RC 회로는 저항 및 커패시턴스 값이 일정하게 유지되는 경우 시간 불변입니다. 이러한 변동이 발생하면 실험 수행 시기에 따라 실험 결과가 달라지므로 시스템은 시간 변형이 됩니다.

시스템 분류-ii

연속 시간 시스템은 연속적인 입력 및 출력 신호를 가지며, 시간은 연속적으로 측정됩니다. 이러한 시스템은 일반적으로 미분 또는 대수 방정식으로 정의됩니다. 예를 들어, RC 회로에서 입력 및 출력 전압 간의 관계는 옴의 법칙과 커패시터 관계에서 파생된 미분 방정식을 통해 표현됩니다.

<img alt="Equation1" src="/files/ftp_upload/16046/16046_PT%20EQUATION_1.svg" style="text-align: center; height: 30px;">

이산 시간 시스템은 특정 구간에서 입력 및 출력 신호를 가지며, 이는 차분 방정식으로 서로 다른 순간에 정의됩니다. 한 가지 예로, 은행 계좌의 월별 잔액에 대한 간단한 모델을 들 수 있으며, 다음과 같이 표현됩니다.

<img alt="Equation2" src="/files/ftp_upload/16046/16046_PT%20EQUATION_2.svg" style="text-align: center; height: 14px;">

여기서 B[n]는 월 n의 잔액이고, D[n]는 입금이며, W[n]는 인출입니다.

시스템은 시간 가변성 또는 시간 불변성으로 분류할 수도 있습니다. 시변 시스템은 시간에 따라 변하는 매개변수를 갖습니다. 연속 시간 시변 시스템은 시변 미분 방정식으로 설명되는 반면, 이산 시간 시변 시스템은 시변 차분 방정식으로 정의됩니다.

시불변 시스템은 입력 신호가 시간 이동될 때 출력 신호에서 동일한 시간 이동을 보입니다. 수학적으로, y(t)가 입력 x(t)에 대한 출력인 경우, 시불변 시스템에서는 y(t−t_0)가 입력 x(t−t_0)에 대한 출력이 됩니다. 예를 들어, 저항 R 및 커패시턴스 C 값이 일정하게 유지되면 RC 회로는 시간 불변입니다. 이러한 값이 변동하면 시스템은 시간 가변적이 되며, 즉 실험이 수행되는 시기에 따라 결과가 달라집니다.

연속 시간 시스템과 이산 시간 시스템, 그리고 시변 시스템과 시불변 시스템의 이러한 차이점을 이해하는 것은 광범위한 엔지니어링 시스템을 분석하고 설계하는 데 매우 중요합니다.

시스템 분류-II

연속 시간 시스템은 연속적으로 측정 된 시간과 함께 연속적인 입력 및 출력 신호를 가지며 일반적으로 차동 또는 대수로 정의됩니다 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Introduction to Signals and Systems

신호 및 시스템 입문

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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

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...

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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