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

Daha düşük örnekleme hızı nedeniyle azaltılmış frekans aralığına sahip azalmış bir sinyal düşünün.
Yeni Nyquist frekansı tarafından belirlenen aralıklarla tekrarlanan spektral kopyaları tanıtan üst örnekleme için her örnek arasına sıfırlar ekleyin.
Sıfır eklenen sekansı, yeni Nyquist sınırında bir kesme frekansına sahip bir alçak geçiren filtreden geçirin. Bu filtre, yalnızca orijinal frekans bileşenlerini koruyarak daha yüksek frekanslı replikaları zayıflatır.
Filtrelenmiş çıkış, orijinal sinyalin etkinliğini koruyarak ve altörnekleme işlemini tersine çevirerek daha yüksek bir örnekleme hızı sinyali üretir.
-4π/9 ile +4π/9 arasında sıfırdan farklı değerler gösteren Fourier dönüşümü olan bir dizi alın.
İkiye kadar alt örnekleyin, böylece -8π/9 ile + 8π/9 arasında değişen bir spektrum elde edin.
Fourier dönüşümünü -π/9 ile + π/9 arasında olacak şekilde sıkıştırarak sekize kadar örnekleyin.
Fourier dönüşümünü -π'dan +π'ye genişletecek şekilde ölçeklendirerek dokuza kadar alt örnekleyin.
Yukarı örneklemeyi dört ve aşağı örneklemeyi dokuz ile birleştirmek, örtüşme olmadan maksimum altörnekleme sağlar.

yukarı Örnekleme

Sinyal bütünlüğünü korumak için dijital sinyal işlemede sinyal örnekleme oranlarını yönetmek esastır. Daha düşük örnekleme oranı nedeniyle seyreltilmiş bir frekans aralığı ile karakterize edilen bir sinyal, her örnek arasına sıfırlar eklenerek yukarı örneklenebilir. Bu yukarı örnekleme süreci orijinal spektrumu genişletir ve yeni Nyquist frekansı tarafından belirlenen aralıklarla tekrarlanan spektral kopyalar sunar. Bu sıfır eklenen diziyi iyileştirmek için yeni Nyquist sınırında bir kesme frekansı ayarlanmış bir alçak geçiş filtresinden geçirilir. Bu filtre, yalnızca orijinal frekans bileşenlerini koruyarak daha yüksek frekanslı kopyaları zayıflatır.

Bu filtreleme sürecinin sonucunda, aşağı örnekleme prosedürünü etkili bir şekilde tersine çevirerek daha yüksek bir örnekleme oranına sahip bir sinyal elde edilir. Örneğin, -2π/9 ile 2π/9 arasında sıfır olmayan değerler gösteren, Fourier dönüşümlü bir diziyi düşünün. Bu dizi dört faktörle aşağı örneklenirse, spektrumu -8π/9'dan 8π/9'a kadar uzanır. Daha sonra, diziyi iki faktörle yukarı örneklendiğinde Fourier dönüşümü sıkıştırılır ve artık -π/9'dan π/9'a kadar değişir.

Bu yukarı örneklenen dizinin dokuz ölçekle daha aşağı örneklenmesi, Fourier dönüşümünün -2π/9'dan 2π/9'a kadar uzamasını sağlar. İki ile yukarı örnekleme ve dokuz ile aşağı örneklemenin bu kombinasyonu, 9/2 faktörüyle aşağı örneklemeye eşdeğerdir ve aliasingden kaçınarak maksimum aşağı örneklemeye ulaşır.

Sıfırlar ekleyerek ve düşük geçişli filtreleme yaparak yukarı örnekleme işlemi ve ardından yukarı örnekleme ve aşağı örneklemenin hassas kombinasyonları, sinyal örnekleme oranlarının etkili bir şekilde yönetilmesini sağlar. Bu yöntem, orijinal sinyalin bütünlüğünün korunmasını sağlayarak farklı örnekleme gereksinimlerine uyum sağlarken aliasing ve bozulmayı önler.

Bu tür teknikler, örnekleme verimliliği ile sinyal doğruluğu arasındaki dengenin çok önemli olduğu dijital sinyal işleme uygulamalarında kritik öneme sahiptir. Bu süreçler boyunca örnekleme oranlarını dikkatlice ayarlayarak orijinal sinyalin temel özelliklerini korumak; iletişim, ses mühendisliği ve veri sıkıştırma gibi çeşitli teknolojik alanlarda doğru sinyal işleme ve yeniden yapılandırmayı kolaylaştırmak mümkündür.

Yukarı Örnekleme

Daha düşük örnekleme hızı nedeniyle azaltılmış frekans aralığına sahip azalmış bir sinyal düşünün.
Üst örnekleme için her örnek arasına sıfırlar ekleyin, bu da ...

Education

JoVE Core

Electrical Engineering

Elektrik Mühendisliği

Unit 1

Ünite 1

Sampling

Örnekleme

KEY TERMS AND CONCEPTS

TEMEL TERİMLER VE KAVRAMLAR

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 Elektrik Mühendisliği, devre analizi teknikleriyle birlikte elektrik devrelerinin temel kavramlarını kapsayan, anlaşılması kolay animasyonlu videolar sunar. Operasyonel amplifikatörler ve devre dönüşümü kavramlarını kullanarak birinci dereceden ve ikinci dereceden devreleri içerir. Pratik tasarım örneklerinin ve gerçek dünya uygulamalarının bilim insanlarınca hazırlanan videolar aracılığıyla dahil edilmesi, karmaşık kavramları erişilebilir hale getirerek önemli bir eğitim değeri katmaktadır.

electrical engineering

HS-PS4-5

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HS-PS4-1

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HS-PS4-3

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HS-PS4-4

Zero-Inserted Signal Reconstruction

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