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

Основными операциями с сигналами являются обращение времени, масштабирование, сдвиг и амплитудные преобразования.
Обращение времени отражает непрерывный сигнал о том, что вертикальная ось в момент времени равна нулю, что достигается путем замены «t» на отрицательную «t». Для рассматриваемого сигнала результаты отображаются графически.
Временное масштабирование сжимает или расширяет сигнал во времени путем замены 't' на 'at', где 'a' является постоянным. Если величина этой константы больше 1, сигнал сжимается; Если оно меньше 1, оно расширяется.
Отрицательное значение этой константы вызывает как обращение времени, так и сжатие или расширение. Это можно графически представить с помощью рассматриваемого сигнала.
Сдвиг времени непрерывного сигнала осуществляется путем замены 't' на 't − t0', где 't0' является постоянным. Положительная постоянная задерживает и смещает сигнал вправо от источника, в то время как отрицательная смещает сигнал вперед и сдвигает его влево.
Амплитудные преобразования сигнала непрерывного времени принимают общий вид, где 'A' и 'B' являются константами. На графике показано амплитудное преобразование сигнала.

Основные операции с сигналами

Basic Operations on Signals

Основные операции с сигналами включают обращение времени, масштабирование времени, сдвиг времени и амплитудные преобразования. Эти операции являются основополагающими в обработке и анализе сигналов.

Обращение времени зеркально отображает непрерывный во времени сигнал относительно вертикальной оси при t=0. Это достигается путем замены t на −t. Например, если рассматривается сигнал x(t), обращенный во времени сигнал будет x(−t). Эту операцию можно графически представить, показав отражённый сигнал.

<img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="height: 150px;">

Масштабирование времени сжимает или расширяет сигнал по времени путем замены t на at, где a — константа. Если ∣a∣&gt;1, сигнал сжимается; если ∣a∣&lt;1, он расширяется. Отрицательное значение a вызывает как обращение времени, так и сжатие или расширение. Графическое представление этой операции с сигналом демонстрирует эти эффекты.

Временной сдвиг непрерывного сигнала выполняется путем замены t на t−t_0, где t_0 — константа. Положительное t_0 задерживает и сдвигает сигнал вправо, а отрицательное t_0 продвигает сигнал вперед и сдвигает его влево. Например, сигнал x(t), смещенный на t_0, представляется как x(t−t_0).

Амплитудные преобразования непрерывного по времени сигнала обычно имеют вид Ax(t)+B, где A и B — константы. Эти преобразования масштабируют амплитуду и могут также сдвигать ее по вертикали. Графически амплитудное преобразование сигнала показывает эффект масштабирования на A и сдвига на B.

Эти основные операции — обращение времени, масштабирование, сдвиг и амплитудные преобразования — являются важными инструментами для модификации и анализа сигналов, позволяя выполнять различные настройки и изменения в приложениях обработки сигналов.

Основными операциями с сигналами являются обращение времени, масштабирование, сдвиг и амплитудные преобразования.
Реверс времени отражает непрерывный сигнал о ...

Education

JoVE Core

Electrical Engineering

Электротехника

Unit 1

Раздел 1

Introduction to Signals and Systems

Введение в сигналы и системы

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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.

Signal Transformations in Time and Amplitude

signal-transformations-in-time-and-amplitude

signal and system

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classification of signals

Signal Types by Time and Amplitude

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Power and Energy in Electrical Signals

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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

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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 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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System Properties: Linearity, Causality, Memory

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key terms and concepts

Learn how time reversal, time scaling, time shifting, and amplitude transformations change continuous-time signals in signal processing and graph form.

Signal Transformations in Time and Amplitude | 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

Signal Transformations in Time and Amplitude

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