Name: modeling pulses with rectangles and triangles
Uploaded: 2025-05-22T09:06:20.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

south-carolina-college-and-career-ready-science-standards

South Carolina College and Career Ready Science Standards

High School

Physics

waves-and-their-applications-in-technologies-for-information-transfer

Waves and Their Applications in Technologies for Information Transfer

P-PS4-5

rectangular-and-triangular-pulse-function

Rectangular and Triangular Pulse Function

単位直交パルス関数は、1単位の高さで原点を中心とする直交関数によって数学的に表されます。
この機能を定義するパラメータは、時間軸に沿ったパルスの中心位置を指定するTと、パルスの持続時間を決定するτの2つです。
例としては、振幅が5V、持続時間が3秒、時間位置が2秒の矩形パルスがあります。このパルスは、矩形関数を使用して表すことができます。
矩形パルスの合成には、2つの時間シフトステップ関数を順次追加するグラフィカルなデモンストレーションが含まれます。
一般的に、単位直交関数は、常に単位ステップ関数を使用して表すことができます。
単位三角関数は、三角関数によって数学的に表現されます。単位の高さがあり、原点を中心としています。
インスタンスは、3 秒に等しい時間を中心とする三角パルスで、振幅は 2、幅は 2 秒です。三角パルスをスケッチするには、すべての t を t-3 に置き換え、幅を 2 に設定します。定義された信号はグラフィカルに示されます。

矩形パルス関数および三角パルス関数

単位矩形パルス関数は、原点を中心とし、高さが 1 単位の矩形関数で数学的に表されます。この関数は、時間軸に沿ったパルスの中心位置を指定する T と、パルスの持続時間を決定する τ の 2 つのパラメータによって定義されます。

たとえば、振幅が 5V、持続時間が 3 秒で中心が t=2 秒の矩形パルスを考えてみましょう。このパルスは、次のように記述される矩形関数を使用して表すことができます。
<img alt="Equation1" src="/files/ftp_upload/16041/16041_PT%20EQUATION_1.svg" style="height: 36px;">

矩形パルスの合成は、2 つの時間シフトされたステップ関数を順番に追加することでグラフで示せます。一般的に、単位矩形関数は常に単位ステップ関数を使用して次のように表すことができます。
<img alt="Equation2" src="/files/ftp_upload/16041/16041_PT%20EQUATION_2.svg" style="height: 36px;">

単位三角関数は、三角関数を使用して数学的に表されます。高さは 1 単位で、原点を中心としています。たとえば、t=3 秒を中心とし、大きさが 2、幅が 2 秒の三角パルスを考えてみましょう。この三角パルスを表現するには、すべての t を t−3 に置き換え、幅を 2 に設定します。定義された信号は次のように記述できます。
<img alt="Equation3" src="/files/ftp_upload/16041/16041_PT%20EQUATION_3.svg" style="height: 36px;">

この三角パルス関数は、高さが中央で 2 に達し、端で 0 に徐々に減少し、合計幅が 2 秒に及ぶ様子をグラフで表すことができます。

単位矩形関数と三角関数はどちらも、さまざまな波形を表す信号処理の基本であり、信号とシステムをモデル化および分析するための複数のアプリケーションで使用されます。これらの関数は、より複雑な信号の動作と操作を理解するために不可欠です。

単位直交パルス関数は、1単位の高さで原点を中心とする直交関数によって数学的に表されます。
2。。。

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

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 at t = 2 seconds can be written with the rectangular function. The same shape can be built graphically by adding two time-shifted step functions in sequence. In general, a unit rectangular function can be written using the unit step function.

The unit triangular function is another common pulse shape. It has unit height and is centered at the origin. For a triangular pulse centered at t = 3 seconds, with a magnitude of 2 and a width of 2 seconds, each t value is replaced with t − 3 and the width is set to 2.

A triangular pulse rises to its peak at the center and then falls to zero at the edges. In this example, the height reaches 2 at the center and spans a total width of 2 seconds. Rectangular and triangular functions are both important in signal processing because they help represent waveforms and support the modeling and analysis of signals and systems. They also provide a foundation for understanding more complex signal behavior and operations.

Modeling Pulses with Rectangles and Triangles

modeling-pulses-with-rectangles-and-triangles

signal and system

Signals and Systems in Everyday Data

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classification of signals

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even and odd signals

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Step, Impulse, and Ramp Signals

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rectangular and triangular pulse function

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

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basic discrete time signals

Discrete-Time Signal Basics and Shapes

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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

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key terms and concepts

Learn how rectangular and triangular pulse functions model signals, use center and width parameters, and connect to step functions in signal processing.

Modeling Pulses with Rectangles and Triangles | 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。

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Modeling Pulses with Rectangles and Triangles

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