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

基本的な信号演算は、時間反転、スケーリング、シフト、振幅変換です。
時間反転は、時間がゼロに等しいときの垂直軸の周りの連続時間信号を反映しており、't' を負の 't' に置き換えることによって実現されます。考慮された信号の場合、結果はグラフィカルに表示されます。
タイムスケーリングは、't' を 'at' ('a' は一定) に置き換えることで、信号を時間的に圧縮または拡張します。この定数の大きさが 1 より大きい場合、信号は圧縮されます。1 未満の場合は、拡張されます。
この定数の負の値は、時間反転と圧縮または拡張の両方を誘発します。これは、考慮された信号を使用してグラフィカルに表すことができます。
連続時間信号のタイムシフトは、「t」を「t − t0」に置き換えることによって行われます。ここで、「t0」は一定です。正の定数は信号を遅延させ、原点から右にシフトし、負の定数は信号を前進させて左にシフトします。
連続時間信号の振幅変換は、「A」と「B」が定数である一般的な形式を取ります。グラフは、例示された信号の振幅変換を示しています。

信号の基本操作

Basic Operations on Signals

基本的な信号操作には、時間反転、時間スケーリング、時間シフト、振幅変換などがあります。これらの操作は、信号処理と分析の基本です。

時間反転は、連続時間信号を t=0 の垂直軸を中心に反転します。これは、t を −t に置き換えることで実現されます。たとえば、信号 x(t) がある場合、時間反転信号は x(−t) になります。この操作は、信号の鏡像をグラフで表すことができます。

<img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="height: 150px;">

時間スケーリングは、t を at に置き換えることで、信号を時間的に圧縮または拡張します。ここで、a は定数です。∣a∣&gt;1 の場合、信号は圧縮され、∣a∣&lt;1 の場合、信号は拡張されます。 a の負の値は、時間の反転と圧縮または拡張の両方を引き起こします。この操作もグラフで示され、信号の変化が視覚的に表現されます。

連続時間信号の時間シフトは、t を t−t_0 に置き換えることによって行われます。ここで、t_0 は定数です。正の t_0 は信号を遅らせて右にシフトし、負の t_0 は信号を進めて左にシフトします。たとえば、t_0 だけシフトされた信号 x(t) は、 x(t−t_0) として表されます。

連続時間信号の振幅変換は、通常、A x(t)+B の形式です。ここで、A と B は定数です。これらの変換は振幅をスケーリングし、垂直方向にシフトすることもできます。信号の振幅変換は、A によるスケーリングと B によるシフトの効果をグラフが示します。

これらの基本操作 (時間反転、スケーリング、シフト、振幅変換) は、信号を操作および分析するための重要なツールであり、信号処理アプリケーションでさまざまな調整や変更を可能にします。

基本的な信号演算は、時間反転、スケーリング、シフト、振幅変換です。
時間反転は、...

Education

JoVE Core

Electrical Engineering

電気工学

Unit 1

ユニット1

Introduction to Signals and Systems

信号とシステム概論

KEY TERMS AND CONCEPTS

主要用語と概念

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

Signals and Systems in Everyday Data

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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

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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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Continuous and Discrete System Models

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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 電気工学 は、電気回路の基本概念と回路解析テクニックを網羅したアニメーションビデオシリーズです。オペアンプと回路変換および 1 次・ 2 次回路の概念を網羅しています。実験を撮影した実写動画では、設計例や現代社会での応用が含まれており、複雑な概念も分かりやすく学習いただけます。

electrical engineering

Signal Transformations in Time and Amplitude

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