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

عمليات الإشارة الأساسية هي انعكاس الوقت ، والقياس ، والتحويل ، وتحويلات السعة.
يعكس انعكاس الوقت إشارة زمنية مستمرة حول المحور الرأسي في الوقت يساوي صفرا ، ويتم تحقيقه عن طريق استبدال "t" بالسالب "t". بالنسبة للإشارة المدروسة ، يتم عرض النتائج بيانيا.
يقوم قياس الوقت بضغط إشارة أو توسيعها في الوقت المناسب عن طريق استبدال "t" ب "at" ، حيث يكون "a" ثابتا. إذا كان حجم هذا الثابت أكبر من 1 ، فإن الإشارة تضغط. إذا كان أقل من 1 ، فإنه يتوسع.
تؤدي القيمة السالبة لهذا الثابت إلى انعكاس الوقت والضغط أو التمدد. يمكن تمثيل ذلك بيانيا باستخدام الإشارة المدروسة.
يتم تغيير الوقت لإشارة زمنية مستمرة عن طريق استبدال "t" ب "t − t0" ، حيث يكون "t0" ثابتا. يؤخر الثابت الموجب الإشارة ويحولها إلى اليمين من الأصل ، بينما يؤدي الثابت السالب إلى تقدم الإشارة وتحويلها إلى اليسار.
تأخذ تحولات السعة لإشارة الوقت المستمر الشكل العام حيث تكون "A" و "B" ثوابتين. يوضح الرسم البياني تحويل السعة لإشارة مثالية.

العمليات الأساسية على الإشارات

Basic Operations on Signals

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 تتضمن العمليات الأساسية للإشارات عكس الزمن، وقياس الزمن، وتحويل الزمن، وتحويلات السعة. هذه العمليات أساسية في معالجة الإشارات وتحليلها.
 
 يعكس عكس الزمن إشارة زمنية متصلة حول المحور الرأسي عند 𝑡=0. ويتحقق ذلك عن طريق استبدال 𝑡 بـ −𝑡. على سبيل المثال، إذا تم اعتبار إشارة 𝑥(𝑡)، فإن الإشارة المعكوسة زمنيًا هي 𝑥(−𝑡). يمكن تمثيل هذه العملية بيانيًا، مع إظهار الإشارة المعكوسة.
 
 <img alt="Figure1" src="/files/ftp_upload/16044/16044_PT%20Figure_1.svg" style="text-align: center; height: 150px;"> 
 يضغط قياس الزمن أو يوسع إشارة في الزمن عن طريق استبدال 𝑡 بـ 𝑎𝑡، حيث 𝑎 ثابت. إذا كانت ∣𝑎∣&gt;1، يتم ضغط الإشارة؛ إذا كان ∣𝑎∣&lt;1، فإنه يتمدد. القيمة السالبة لـ 𝑎 تسبب كل من عكس الزمن والضغط أو التمدد. يوضح التمثيل البياني لهذه العملية على إشارة هذه التأثيرات.
 
 يتم تحويل الزمن لإشارة زمنية متصلة عن طريق استبدال 𝑡 بـ 𝑡−𝑡_0,، حيث 𝑡_0 ثابت. تؤخر 𝑡_0 الموجبة الإشارة وتحولها إلى اليمين، بينما تقدم 𝑡_0 السالبة الإشارة وتحولها إلى اليسار. على سبيل المثال، يتم تمثيل الإشارة 𝑥(𝑡) المحولة بواسطة 𝑡_0 على أنها 𝑥(𝑡−𝑡_0).
 
 
 تكون تحويلات السعة لإشارة زمنية متصلة بشكل عام على هيئة 𝐴𝑥(𝑡)+𝐵، حيث 𝐴 و𝐵 ثابتان. تعمل هذه التحويلات على تغيير حجم السعة ويمكنها أيضًا تحريكها رأسيًا. من الناحية الرسومية، يُظهر تحويل سعة الإشارة تأثير التغيير بواسطة 𝐴 والتحويل بواسطة 𝐵.
 
 
 هذه العمليات الأساسية - عكس الزمن، والتغيير، والتغيير، وتحويلات السعة - هي أدوات أساسية للتلاعب بالإشارات وتحليلها، مما يسمح بإجراء تعديلات وتعديلات مختلفة في تطبيقات معالجة الإشارات.
 
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عمليات الإشارة الأساسية هي انعكاس الوقت ، والقياس ، والتحويل ، وتحويلات السعة.
يعكس انعكاس الوقت إشارة زمنية مستمرة حول ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Introduction to Signals and Systems

مقدمة في الإشارات والأنظمة

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

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

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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...

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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

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even and odd signals

Signal Symmetry and Decomposition

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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

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...

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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 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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