Name: zero-inserted signal reconstruction
Uploaded: 2024-09-26T13:17:07.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

Next Generation Science Standards

High School

Physical Science

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

Waves and Their Applications in Technologies for Information Transfer

HS-PS4-2

Upsampling

ضع في اعتبارك إشارة مهتلئة ذات نطاق تردد منخفض بسبب انخفاض معدل أخذ العينات.
أدخل أصفارا بين كل عينة لأخذ عينات ، والتي تقدم نسخا متماثلة طيفية متكررة على فترات تحددها تردد Nyquist الجديد.
قم بتمرير التسلسل الذي تم إدخاله صفريا عبر مرشح التمرير المنخفض بتردد قطع عند حد Nyquist الجديد. يخفف هذا المرشاح من النسخ المتماثلة عالية التردد ، ويحتفظ فقط بمكونات التردد الأصلية.
ينتج الإخراج الذي تمت تصفيته إشارة معدل أخذ عينات أعلى ، مما يحافظ على فعالية الإشارة الأصلية ويعكس عملية أخذ العينات المنخفضة.
خذ تسلسلا مع تحويل فورييه يظهر قيما غير صفرية من -4π/9 إلى +4π/9.
قم بتقليل عينتها بمقدار اثنين ، مما ينتج عنه طيف يمتد من -8π/9 إلى +8π/9.
قم برفع عينته بمقدار ثمانية ، مع ضغط تحويل فورييه ليمتد من -π/9 إلى + π/9.
قم بتقليل عينتها بمقدار تسعة ، وقم بتغيير حجم تحويل فورييه ليمتد من -π إلى +π.
يؤدي الجمع بين أخذ العينات الصاعدة بمقدار أربعة وتقليل العينات بمقدار تسعة إلى الحد الأقصى لتقليل العينات دون التعرج.

رفع العينات

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إن إدارة معدلات أخذ العينات من الإشارات أمر ضروري في معالجة الإشارات الرقمية للحفاظ على سلامة الإشارة. يمكن رفع العينات من إشارة مقطوعة، تتميز بنطاق تردد مخفض بسبب معدل أخذ العينات المنخفض، عن طريق إدخال أصفار بين كل عينة. تعمل عملية رفع العينات هذه على توسيع الطيف الأصلي وإدخال نسخ طيفية متكررة على فترات زمنية تمليها تردد نيستكويست الجديد. لتحسين هذا التسلسل الذي تم إدخال صفر فيه، يتم تمريره عبر مرشح تمرير منخفض بتردد قطع مضبوط عند حد نيستكويست الجديد. يعمل هذا المرشح على إضعاف النسخ ذات التردد الأعلى، مع الحفاظ فقط على مكونات التردد الأصلية.

وتكون نتيجة عملية الترشيح هذه إشارة بمعدل أخذ عينات أعلى تعكس بشكل فعال إجراء خفض العينات. على سبيل المثال، ضع في اعتبارك تسلسلًا به تحويل فورييه يعرض قيمًا غير صفرية من -2π/9 إلى 2π/9. إذا تم تقليل حجم هذا التسلسل بمقدار أربعة أضعاف، فإن طيفها يمتد من -8π/9 إلى 8π/9. بعد ذلك، يؤدي رفع حجم التسلسل بمقدار اثنين إلى ضغط تحويل فورييه، الذي يتراوح الآن من -π/9 إلى π/9.

يؤدي خفض حجم التسلسل الذي تم رفع حجمه بمقدار تسعة إلى توسيع تحويل فورييه ليمتد من -2π/9 إلى 2π/9. إن هذا الجمع بين رفع حجم التسلسل بمقدار اثنين وخفض حجم التسلسل بمقدار تسعة يعادل خفض حجم التسلسل بمقدار 9/2، مما يحقق أقصى قدر من خفض حجم التسلسل دون إدخال تعرجات.

إن عملية رفع العينات عن طريق إدخال الأصفار ثم الترشيح منخفض التردد، متبوعة بمجموعات دقيقة من رفع حجم التسلسل وخفض حجم التسلسل، تسمح بإدارة فعّالة لمعدلات أخذ العينات من الإشارة. تضمن هذه الطريقة الحفاظ على سلامة الإشارة الأصلية، ومنع التعرج والتشويه أثناء التكيف مع متطلبات أخذ العينات المختلفة.

تعتبر مثل هذه التقنيات بالغة الأهمية في تطبيقات معالجة الإشارات الرقمية، حيث يكون التوازن بين كفاءة أخذ العينات ودقة الإشارة أمرًا بالغ الأهمية. ومن خلال ضبط معدلات أخذ العينات بعناية من خلال هذه العمليات، من الممكن الحفاظ على الخصائص الأساسية للإشارة الأصلية، مما يسهل معالجة الإشارات وإعادة بنائها بدقة في مختلف المجالات التكنولوجية، بما في ذلك الاتصالات وهندسة الصوت وضغط البيانات.

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ضع في اعتبارك إشارة مهتلئة ذات نطاق تردد منخفض بسبب انخفاض معدل أخذ العينات.
أدخل الأصفار بين كل عينة إلى أعلى عينة ، والتي تقدم ...

Education

JoVE Core

Electrical Engineering

الهندسة الكهربائية

Unit 1

الوحدة الأولى

Sampling

أخذ العينات

KEY TERMS AND CONCEPTS

المصطلحات والمفاهيم الأساسية

zero-inserted signal reconstruction

Zero-inserted signal reconstruction is a digital signal processing method used to raise a signal’s sampling rate while keeping its important frequency content. A decimated signal has fewer samples and a narrower frequency range. To upsample it, zeros are inserted between the original samples.

This zero-stuffed sequence changes the spectrum. It creates repeated spectral replicas at intervals set by the new Nyquist frequency, which is the highest frequency allowed by the new sampling rate. A lowpass filter is then applied with a cutoff at that new Nyquist limit. The filter reduces the higher-frequency replicas and preserves the original signal components.

The filtered result is a higher-rate signal that effectively reverses the earlier downsampling step. The transcript also shows how sampling-rate changes can be combined. A signal with non-zero Fourier values from −2π/9 to 2π/9 becomes wider after downsampling by four. Upsampling that signal by two compresses the Fourier transform to −π/9 to π/9, and a later downsampling by nine extends it back to −2π/9 to 2π/9.

That sequence of upsampling by two and downsampling by nine is equivalent to downsampling by 9/2. It gives the maximum downsampling possible without aliasing, which is frequency overlap that can distort a signal. These steps are important in communications, audio engineering, and data compression, where signal fidelity must be protected while sampling rates are adjusted.

Zero-Inserted Signal Reconstruction

sampling theorem

Sampling Signals for Digital Use

Sampling signals for digital use turns a continuous-time signal, x(t), into a discrete-time signal. This step is essential when a real-world signal must be stored or processed by a digital system. A train of impulses sets the sampling interval, and the sampling frequency describes how often the signal is measured. The sampling process works by multiplying the continuous-time signal by the impulse train. This creates a series of discrete impulses called the sampled signal. Engineers then study...

sampling continuous time signal

Impulse-Train Sampling and Zero-Order Hold

Impulse-train sampling and zero-order hold are two key steps in digital signal processing. Together, they show how a continuous-time signal can be turned into samples and then built back into a continuous-looking waveform. Impulse-train sampling uses a periodic impulse train. This train is a series of delta functions placed at regular intervals set by the sampling period. When the continuous-time signal is multiplied by the impulse train, the result is a set of impulses whose amplitudes match...

reconstruction of signal using interpolation

reconstruction-of-signal-using-interpolation

Signal Reconstruction with Low-Pass Filtering

Signal reconstruction with low-pass filtering helps turn a sampled signal back into a smooth continuous signal. When a continuous signal is sampled with a period T, the sampled version creates replicas of the original spectrum in the frequency domain. These replicas are spaced by the sampling frequency. A zero-order hold can be used to process the sampled signal. This method keeps each sample value until the next sampling period, so the output becomes piecewise constant. In the frequency...

aliasing

Sampling Signals Without Aliasing

Sampling a signal at the right rate is essential for accurate signal reconstruction. A time-domain signal can be analyzed with its Fourier transform, which reveals its spectrum. When the signal is sampled, the spectrum becomes multiple scaled replicas in the frequency domain. The spacing between these replicas depends on the sampling frequency. If the sampling frequency is below the Nyquist rate, the replicas overlap. The Nyquist rate is twice the highest frequency in the original signal. Once...

downsampling

Decimation and Sampling Rate Reduction

Decimation reduces a sampled sequence by keeping every N-th sample. At those integer multiples of N, the original and reduced sequences match. This makes the sequence shorter and more efficient for digital signal processing. The Fourier transform of a decimated sequence is not just a simple copy of the original. It becomes a scaled and shifted combination of the original spectrum. In effect, the reduced sequence reflects the same frequency content, but in a form shaped by the new sampling...

upsampling

Zero-inserted signal reconstruction is a digital signal processing method used to raise a signal’s sampling rate while keeping its important frequency content. A decimated signal has fewer samples and a narrower frequency range. To upsample it, zeros are inserted between the original samples. This zero-stuffed sequence changes the spectrum. It creates repeated spectral replicas at intervals set by the new Nyquist frequency, which is the highest frequency allowed by the new sampling rate. A...

bandpass sampling

Sampling Narrow Frequency Bands

Bandpass sampling is a signal processing method for signals whose energy is concentrated in a narrow frequency band. Such a signal is called a bandpass signal. The method works when the sampling rate is greater than twice the signal bandwidth, which helps prevent aliasing. A bandpass signal has a spectrum with a lower limit, ω1, and an upper limit, ω2. Its spectrum is nonzero only between those two frequencies. To sample it, the time-domain signal is multiplied by an impulse train. This...

key terms and concepts

Learn how zero insertion and lowpass filtering rebuild a signal at a higher sampling rate while reducing spectral replicas and avoiding aliasing.

Zero-Inserted Signal Reconstruction | 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

HS-PS4-5

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Echo

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HS-PS4-1

The Electromagnetic Spectrum

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Discrete Fourier Transform

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However, in reality, the sensor can only ...

Discrete-Time Fourier Series

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Calculating the expansion ...

Sampling Theorem

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Properties of Fourier Transform I

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Methods of Documentation VII: EMR

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Fast Fourier Transform

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Reconstruction of Signal using Interpolation

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Downsampling

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Design Example

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Properties of DTFT I

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Relation of DFT to z-Transform

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Properties of the z-Transform I

Certain properties provide a solid foundation for analyzing discrete-time systems using the Z-transform.
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Concept of Resonance and its Characteristics

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Interference and Diffraction

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Interference and diffraction ...

Reflection and Refraction

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...

Electromagnetic Fields

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Photoelectric Effect

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HS-PS4-3

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Determination Of NOx in Automobile Exhaust Using UV-VIS Spectroscopy

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Introduction to the Spectrophotometer

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Evaluate the validity and reliability of claims in published materials of the effects that different frequencies of electromagnetic radiation have when absorbed by matter. [Clarification Statement: Emphasis is on the idea that photons associated with different frequencies of light have different energies, and the damage to living tissue from electromagnetic radiation depends on the energy of the radiation. Examples of published materials could include trade books, magazines, web resources, videos, and other passages that may reflect bias.] [Assessment Boundary: Assessment is limited to qualitative descriptions.]

HS-PS4-4

Zero-Inserted Signal Reconstruction

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