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

שקול אות שהושמד עם טווח תדרים מופחת בשל קצב הדגימה הנמוך שלו.
הוסף אפסים בין כל דגימה ל- upsample, המציג העתקים ספקטרליים חוזרים ונשנים במרווחי זמן שנקבעו על ידי תדר Nyquist החדש.
העבר את הרצף שהוכנס לאפס דרך מסנן מעבר נמוך עם תדירות חיתוך בגבול Nyquist החדש. מסנן זה מחליש עותקים משוכפלים בתדר גבוה יותר, ושומר רק על רכיבי התדר המקוריים.
הפלט המסונן מפיק אות בקצב דגימה גבוה יותר, שומר על יעילות האות המקורי והופך את תהליך הפחתת הדגימה.
קח רצף עם התמרת פורייה המציגה ערכים שאינם אפס מ- -4π/9 עד +4π/9.
צמצמו את הדגימה בשניים, והתוצאה היא ספקטרום המשתרע בין -8π/9 ל + 8π/9.
הגדילו אותו בשמונה, דחסו את התמרת פורייה לטווח שבין -π/9 ל-+ π/9.
צמצמו את הדגימה בתשע, והגדילו את התמרת פורייה כך שתתארך מ-π- ל-π+.
שילוב של הגדלת הדגימה בארבע ודגימת הפחתה בתשע נותן את דגימת ההפחתה המקסימלית ללא החלקה.

דגימת-יתר (upsampling)

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 ניהול קצבי דגימה של אותות הוא עניין חיוני בעיבוד אותות דיגיטליים על מנת לשמור על שלמות האות. ניתן להגדיל את קצב הדגימה של אות מדולל, המאופיין בטווח תדרים מופחת עקב קצב דגימה נמוך יותר, באמצעות הכנסה של אפסים בין כל דגימה. תהליך זה של דגימת-יתר (Upsampling) מרחיב את הספקטרום המקורי ומוסיף שכפולים ספקטרליים חוזרים במרווחים הנקבעים על ידי תדירות נייקוויסט החדשה. כדי לחדד את הרצף שבו הוכנסו אפסים, הוא מועבר דרך מסנן מעבר נמוך עם תדר חיתוך המוגדר בגבול נייקוויסט החדש. מסנן זה מחליש את השכפולים בעלי התדר הגבוה יותר, תוך שימור רכיבי התדר המקוריים בלבד.
 
 התוצאה של תהליך הסינון הזה היא אות עם קצב דגימה גבוה יותר, המהווה למעשה הפיכה של תהליך הדילול (downsampling). לדוגמה, נבחן רצף עם התמרת פורייה המראה ערכים שונים מאפס בטווח של 2π/9- עד 2π/9. אם רצף זה מדולל (downsampled) על ידי גורם של ארבע, ספקטרום האות יתפרש מ-8π/9- עד 8π/9. לאחר מכן, דגימת יתר של הרצף הזה על ידי גורם של שניים דוחסת את התמרת פורייה לטווח של π/9- עד π/9.
 
 דגימה חסרה נוספת של הרצף הדגום בדגימת יתר על ידי גורם של תשע, גורמת להתמרת פורייה להתרחב שוב לטווח של 2π/9- עד 2π/9. שילוב זה של דגימה יתרה על ידי שניים ודגימה חסרה על ידי תשע שווה ערך לדגימה חסרה על ידי גורם של 9/2, ומשיג את הדילול המקסימלי מבלי להכניס קיפול תדרים (aliasing).
 
 תהליך של דגימת יתר על ידי הכנסת אפסים ולאחר מכן סינון באמצעות מסנן מעבר נמוך, יחד עם שילובים מדויקים של דגימת יתר ודילול, מאפשר ניהול יעיל של קצבי הדגימה של אותות. שיטה זו מבטיחה שלמות האות המקורי נשמרת, תוך מניעת קיפול תדרים ועיוותים, תוך התאמה לדרישות שונות של קצב דגימה.
 
 טכניקות כאלו הן קריטיות ביישומי עיבוד אותות דיגיטליים, שבהם איזון בין יעילות הדגימה לשלמות האות הוא חשוב ביותר. על ידי התאמה מדויקת של קצבי הדגימה באמצעות תהליכים אלו, ניתן לשמר את המאפיינים החיוניים של האות המקורי, ולהקל על עיבוד אותות ושחזורם בצורה מדויקת במגוון תחומים טכנולוגיים, כולל תקשורת, הנדסת שמע ודחיסת נתונים.
 
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דגימת-יתר (Upsampling)

שקול אות שהושמד עם טווח תדרים מופחת בשל קצב הדגימה הנמוך שלו.
הוסף אפסים בין כל מדגם ל- upsample, המציג ...

Education

JoVE Core

Electrical Engineering

הנדסה חשמלית

Unit 1

יחידה 1

Sampling

דגימה

KEY TERMS AND CONCEPTS

מונחי מפתח ומושגים

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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HS-PS4-1

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HS-PS4-4

Zero-Inserted Signal Reconstruction

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