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

샘플링 속도가 낮기 때문에 주파수 범위가 감소한 데시메이션된 신호가 있다고 생각해 보십시오.
업샘플링할 각 샘플 사이에 0을 삽입하면 새로운 나이퀴스트 주파수에 의해 결정된 간격으로 반복되는 스펙트럼 복제본이 발생합니다.
0으로 삽입된 시퀀스를 새로운 나이퀴스트 한계에서 차단 주파수를 갖는 저역통과 필터를 통과시킵니다. 이 필터는 더 높은 주파수의 반복 회로를 감쇠시켜 원래 주파수 성분만 유지합니다.
필터링된 출력은 더 높은 샘플링 속도 신호를 생성하여 원래 신호를 효과적으로 유지하고 다운샘플링 프로세스를 반전시킵니다.
-4π/9에서 +4π/9 사이의 0이 아닌 값을 표시하는 푸리에 변환이 있는 시퀀스를 가져옵니다.
2로 다운샘플링하면 -8π/9에서 + 8π/9까지의 스펙트럼이 생성됩니다.
푸리에 변환을 -π/9에서 + π/9로 압축하여 8로 업샘플링합니다.
9로 다운샘플링하여 푸리에 변환을 -π에서 +π로 확장하도록 스케일링합니다.
업샘플링을 4로 결합하고 다운샘플링을 9로 결합하면 앨리어싱 없이 최대 다운샘플링을 얻을 수 있습니다.

업샘플링

신호 무결성을 유지하기 위해 디지털 신호 처리에서 신호 샘플링 속도를 관리하는 것은 필수적입니다. 낮은 샘플링 속도로 인해 주파수 범위가 감소한 데시메이션된 신호는 각 샘플 사이에 0을 삽입하여 업샘플링할 수 있습니다. 이 업샘플링 과정은 원래 스펙트럼을 확장하고 새로운 나이퀴스트 주파수에 의해 결정된 간격으로 반복되는 스펙트럼 복제본을 도입합니다. 이 0 삽입 시퀀스를 정제하기 위해 새로운 나이퀴스트 한계로 설정된 차단 주파수를 사용하여 저역 통과 필터를 통과합니다. 이 필터는 더 높은 주파수 복제본을 감쇠시켜 원래 주파수 구성 요소만 보존합니다.

이 필터링 과정의 결과는 다운샘플링 절차를 효과적으로 역전시키는 더 높은 샘플링 속도의 신호입니다. 예를 들어, −2π/9에서 2π/9까지 0이 아닌 값을 나타내는 푸리에 변환이 있는 시퀀스를 고려합니다. 이 시퀀스를 4배로 다운샘플링하면 스펙트럼은 −8π/9에서 8π/9까지가 됩니다. 그 후 시퀀스를 2배로 업샘플링하면 푸리에 변환이 압축되어 이제 범위가 -π/9에서 π/9가 됩니다.

이 업샘플링된 시퀀스를 9배로 더 다운샘플링하면 푸리에 변환이 -2π/9에서 2π/9로 확장됩니다. 2배로 업샘플링하고 9배로 다운샘플링하는 이 조합은 9/2배로 다운샘플링하는 것과 동일하여 앨리어싱을 도입하지 않고 최대 다운샘플링을 달성합니다.

0을 삽입하고 저역 통과 필터링을 한 다음 업샘플링과 다운샘플링을 정확하게 조합하여 신호 샘플링 속도를 효과적으로 관리할 수 있습니다. 이 방법은 원래 신호의 무결성이 유지되도록 하여 앨리어싱과 왜곡을 방지하는 동시에 다양한 샘플링 요구 사항에 적응합니다.

이러한 기술은 샘플링 효율성과 신호 충실도 간의 균형이 가장 중요한 디지털 신호 처리 애플리케이션에서 매우 중요합니다. 이런 과정을 통해 샘플링 속도를 신중하게 조정함으로써 원래 신호의 필수적인 특성을 유지할 수 있으며, 통신, 오디오 엔지니어링, 데이터 압축을 포함한 다양한 기술 분야에서 정확한 신호 처리와 재구성이 용이해집니다.

샘플링 속도가 낮기 때문에 주파수 범위가 감소한 데시메이션된 신호가 있다고 생각해 보십시오.
업샘플링할 각 샘플 사이에 0을 삽입하면 ...

Education

교육

JoVE Core

Electrical Engineering

전기공학

Unit 1

제1단원

Sampling

표본 추출

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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-PS4-4

Zero-Inserted Signal Reconstruction

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