Name: dtft signal properties and frequency effects
Uploaded: 2024-09-26T13:17:04.000Z
Duration: 1 min 24 s
Channel: JoVE

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Next Generation Science Standards

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Waves and Their Applications in Technologies for Information Transfer

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Properties of DTFT I

ضع في اعتبارك إشارتين زمنيتين منفصلتين ، لكل منهما DTFTs الخاصة بتحويلات فورييه المنفصلة في الوقت المنفصل.
يتم ضرب الإشارات أولا في الثوابت a و b ، ثم يتم دمجها لتشكيل إشارة ناتجة.
يؤدي تطبيق DTFT على الإشارة الناتجة إلى تحويلها إلى DTFT جديد ، مما يدل على خاصية الخطية.
عندما تتأخر الإشارة بعدد معين من الوحدات ، فإن DTFT الخاص بها يتعرض لتحول طور يتناسب مع التأخير ، والمعروف باسم خاصية تغيير الوقت.
تحدث خاصية تحويل التردد عندما يتم ضرب إشارة المجال الزمني في أس معقد يغير مكونات تردد الإشارة.
يظهر انعكاس الوقت أن عكس إشارة الوقت المنفصل في الوقت يؤدي إلى تمثيل مجال تردد ينعكس حول المحور الرأسي.
وتكشف خاصية الاقتران أن أخذ الاقتران المركب للإشارة يؤدي إلى انعكاس واقتران مكونات التردد في مجال التردد.
عندما يتم قياس الإشارة بواسطة عامل k ، فإنها تحتفظ بالقيم فقط على فترات مضاعفة k.
يؤدي حساب DTFT لهذه الإشارة إلى ضغط مكونات التردد بمقدار k ، مما يدل على خاصية قياس الوقت.

خصائص تحويل فورييه المنفصل للزمن 1

<div style="direction: rtl;">
في معالجة الإشارات، تلعب تحويلات فورييه المنفصلة للزمن (DTFTs) دورًا بالغ الأهمية في تحليل الإشارات المنفصلة للزمن في مجال التردد. تساعد خصائص تحويلات فورييه المنفصلة للزمن المختلفة مثل الخطية، والتحول الزمني، والتحول الترددي، وعكس الزمن، والاقتران، وقياس الزمن في فهم هذه الإشارات والتلاعب بها لتطبيقات مختلفة.

خاصية الخطية لتحويلات فورييه المنفصلة للزمن أساسية. إذا تم ضرب إشارتين منفصلتين للزمن بالثوابت 𝑎 وb على التوالي، ثم دمجهما لتكوين إشارة محصلة، فإن تحويل فورييه المنفصل للزمن لهذه الإشارة المحصلة هو المجموع المرجح لتحويلات فورييه المنفصلة للزمن للإشارات الفردية.

<img alt="Equation1" src="/files/ftp_upload/16072/16072_PT%20EQUATION_1.svg" style="text-align: center; height: 26px;">
تشير خاصية التحويل الزمني في تحويلات فورييه الرقمية إلى أن تأخير الإشارة بمقدار 𝑛_0 وحدة في المجال الزمني يؤدي إلى تحول طوري بمقدار e^−jωn0 في تحويلات فورييه الرقمية.

<img alt="Equation2" src="/files/ftp_upload/16072/16072_PT%20EQUATION_2.svg" style="text-align: center; height: 22px;">
تحدث خاصية تحويل التردد عندما يتم ضرب إشارة زمنية منفصلة 𝑥[𝑛] في أسية مركبة e^jω0n. يؤدي هذا الضرب إلى تحويل مكونات التردد للإشارة بمقدار 𝜔_0.

يظهر عكس الوقت خاصية أخرى رائعة. إذا تم عكس إشارة x[n] في الوقت، أي 𝑥[−𝑛]، فإن تمثيل مجال التردد الخاص بها ينعكس حول نقطة الأصل.

تكشف خاصية الاقتران أن أخذ المرافق المركب لإشارة x[n]، والمشار إليه بـ 𝑥∗[𝑛]، يؤدي إلى DTFT 𝑋∗(𝑒^−𝑗𝜔)، والذي يعكس ويرافق مكونات التردد.

وأخيرًا، توضح خاصية قياس الوقت أنه إذا تم قياس إشارة زمنية منفصلة بعامل k، فإن الإشارة تحتفظ بالقيم فقط عند فترات مضاعفات k. يضغط DTFT للإشارة المقاسة 𝑥[𝑘𝑛] مكونات التردد بمقدار k. وبالتالي، فإن DTFT لـ 𝑥[𝑘𝑛] هو 𝑋(𝑒^𝑗𝜔𝑘)، مما يوضح ضغط مكونات التردد بعامل 𝑘.

إن فهم هذه الخصائص يسمح بمعالجة الإشارة بكفاءة، مما يساعد في تطبيقات مختلفة مثل الترشيح والتعديل وتحليل الإشارة.

</div>

ضع في اعتبارك إشارتين زمنيتين منفصلتين ، لكل منهما DTFTs الخاصة بتحويلات فورييه المنفصلة في الوقت المنفصل.
يتم ضرب الإشارات أولا في الثوابت a و ...

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dtft signal properties and frequency effects

Discrete-Time Fourier Transforms (DTFTs) help describe discrete-time signals in the frequency domain. The main DTFT properties include linearity, time shifting, frequency shifting, time reversal, conjugation, and time scaling. These rules make it easier to analyze and change signals in signal processing.

Linearity is the most basic property. If two discrete-time signals are multiplied by constants a and b and then added together, the DTFT of the result is the weighted sum of the two individual DTFTs. This property is useful when signals are combined before analysis.

Time shifting changes a signal’s position in time. When a signal is delayed by n0 units, its DTFT gains a phase factor of e^−jωn0. Frequency shifting works differently. If a discrete-time signal x[n] is multiplied by the complex exponential ejω0n, its frequency components shift by ω0.

Time reversal flips the signal in time. If x[n] becomes x[−n], its frequency-domain form is reflected around the origin. Conjugation also changes the DTFT shape. Taking the complex conjugate x*[n] gives X*(e^−jω), which reflects and conjugates the frequency components.

Time scaling shows how stretching or compressing time changes frequency. If a discrete-time signal is scaled by a factor k, the signal keeps values only at intervals that are multiples of k. The DTFT of x[kn] becomes X(ejωk), which compresses the frequency components by the factor k. These DTFT properties are useful in filtering, modulation, and signal analysis.

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Discrete-Time Fourier Transforms (DTFTs) help describe discrete-time signals in the frequency domain. The main DTFT properties include linearity, time shifting, frequency shifting, time reversal, conjugation, and time scaling. These rules make it easier to analyze and change signals in signal processing. Linearity is the most basic property. If two discrete-time signals are multiplied by constants a and b and then added together, the DTFT of the result is the weighted sum of the two individual...

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DTFT Signal Properties and Frequency Effects

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