Name: discrete-time signal basics and shapes
Uploaded: 2024-09-26T13:16:53.000Z
Duration: 1 min 16 s
Channel: JoVE

يتم التعبير عن تسلسل خطوة الوحدة ك 1 للصفر والقيم الموجبة للعدد الصحيح "n". يمكن عرض هذا بيانيا باستخدام مجموعة من ثماني نقاط عينة.
يتم التعبير عن دافع الوحدة أو تسلسل العينة رياضيا لجميع القيم المنفصلة ل n. إنه صفر لجميع القيم "n" باستثناء الصفر.
دافع الوحدة هو الفرق الأول لخطوة الوحدة ، بينما خطوة الوحدة هي المجموع التراكمي لعينة الوحدة. يتم توضيح هذا الارتباط بصريا من خلال رسم بياني.
يمكن لتسلسل نبضة الوحدة أن يأخذ عينة فعالة من قيمة الإشارة عند n يساوي صفرا لأنها غير صفرية فقط عند تلك النقطة.
يظهر تسلسل منحدر الوحدة تصعيدا خطيا في القيمة مع الزيادة في عدد العينة. بالنسبة لسلسلة من 12 عينة على منحدر وحدة ، يوضح الرسم البياني زيادة خطية في السعة مع رقم العينة.
يتم تحديد التسلسل الجيبي من خلال اتساعه ومعلمات الطور.
يتم تعريف التسلسل الأسي باستخدام الأعداد المركبة ، مع تمثيل التسلسلات المتحللة والمتزايدة بشكل كبير على الرسم البياني.

إشارات الوقت المنفصلة الأساسية

Basic Discrete Time Signals

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يتم تعريف تسلسل الخطوة الوحدوية على أنه 1 للقيم الصفرية والموجبة للعدد الصحيح n. يمكن عرض هذا التسلسل بيانياً باستخدام مجموعة من ثماني نقاط عينة، مع إظهار دالة خطوة تبدأ من n=0 وتبقى ثابتة بعد ذلك.

يُعبَّر عن تسلسل النبضة الوحدوية أو العينة رياضياً على أنه صفر لجميع قيم n باستثناء n=0، حيث يكون 1. تسلسل النبضة الوحدوية، الذي يشار إليه بـ δ(n)، هو أول فرق لتسلسل الخطوة الوحدوية، بينما تسلسل الخطوة الوحدوية u(n) هو المجموع التراكمي لتسلسل النبضة الوحدوية. يمكن توضيح هذه العلاقة بصريًا من خلال رسم بياني، مما يسلط الضوء على كيفية قدرة النبضة الوحدوية على أخذ عينات من قيمة الإشارة بشكل فعال عند n=0.

يظهر تسلسل منحدر الوحدة زيادة خطية في القيمة مع زيادة رقم العينة. على سبيل المثال، سيظهر تسلسل مكون من 12 عينة على منحدر الوحدة زيادة خطية في السعة مع كل رقم عينة، ويتم تمثيله بيانياً بخط مستقيم.

يتم تعريف التسلسل الجيبي من خلال معلمات السعة والطور. يمكن تمثيل هذا التسلسل على النحو التالي،

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_1.svg" style="text-align: center; height: 14px;">
حيث A هي السعة، وω هو التردد الزاوي، وΦ هو الطور.

يتم تعريف التسلسل الأسي باستخدام الأعداد المركبة، مع تمثيل التسلسلات المتناقصة والمتزايدة بشكل أسي على الرسم البياني. يمكن كتابة التسلسل المتناقص بشكل أسي على النحو التالي،

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_2.svg" style="text-align: center; height: 14px;">
بينما يتم التعبير عن التسلسل المتزايد بشكل أسي على النحو التالي،

<img alt="Equation1" src="/files/ftp_upload/16043/16043_PT%20EQUATION_3.svg" style="text-align: center; height: 14px;">
حيث A هي السعة الأولية وα هو ثابت موجب. تعتبر هذه التسلسلات أساسية في تحليل تطبيقات معالجة الإشارات المختلفة نظرًا لخصائصها وسلوكياتها الفريدة.

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يتم التعبير عن تسلسل خطوة الوحدة ك 1 للصفر والقيم الموجبة للعدد الصحيح "n". يمكن عرض هذا بيانيا باستخدام مجموعة من ثمانية ...

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

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 cumulative sum of the unit impulse sequence. A graph can show how the impulse samples the signal value at n = 0.

The unit ramp sequence increases linearly as the sample number increases. For example, a 12-sample ramp rises by the same amount at each sample, so its graph appears as a straight line. This makes the ramp easy to recognize on a plot.

A sinusoidal sequence is set by its amplitude and phase. In the expression for this sequence, A is the amplitude, ω is the angular frequency, and Φ is the phase. An exponential sequence uses complex numbers. It can describe both exponentially decaying and exponentially increasing sequences. The decaying form and the increasing form are both shown on graphs, with A as the initial amplitude and α as a positive constant. These basic sequences are important because they help describe many signal-processing applications.

Discrete-Time Signal Basics and Shapes

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Complex Exponentials in Signal Behavior

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basic discrete time signals

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...

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electrical engineering

Discrete-Time Signal Basics and Shapes

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