Name: decimation and sampling rate reduction
Uploaded: 2024-09-26T13:17:07.000Z
Duration: 1 min 20 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

Downsampling

Considere una secuencia muestreada con valores cero entre instantes de muestreo. Reemplácelo tomando cada N-ésimo valor de la secuencia muestreada.
Las secuencias original y muestreadas son iguales en múltiplos enteros de N.
La diezmación extrae cada N-ésima muestra de una secuencia, lo que hace que la nueva secuencia sea más eficiente.
La transformada de Fourier de la secuencia diezmada es una combinación de versiones escaladas y desplazadas del espectro original.
Esta transformación simplifica el análisis centrándose en intervalos distintos de cero.
La relación final muestra que la transformada de Fourier de la secuencia diezmada es una versión a escala de la transformada original.
Esta escala enfatiza la naturaleza periódica introducida por la diezmación, con espectros que difieren solo en la escala de frecuencia.
Si el espectro original está limitado por la banda sin aliasing, la diezmación extiende el espectro a una banda de frecuencia más grande.
El diezmado de una secuencia de una señal de tiempo continuo reduce la frecuencia de muestreo en un factor de N, evitando el solapamiento si la señal original está sobremuestreada.
Cuando se interpreta la secuencia original como muestras de una señal de tiempo continuo, la diezmación se denomina reducción de muestreo.

reducción de la resolución de muestreo

Al considerar una secuencia muestreada con valores cero entre instantes de muestreo, se puede reemplazar tomando cada N-ésimo valor de la secuencia. En estos múltiplos enteros de N, las secuencias original y muestreada coinciden. Este proceso, conocido como diezmado, implica extraer cada N-ésima muestra de una secuencia, creando así una secuencia más eficiente.
La transformada de Fourier de la secuencia diezmada revela una combinación de versiones escaladas y desplazadas del espectro original. Esta transformación se centra en los intervalos distintos de cero de la secuencia, simplificando el análisis. La relación entre las transformadas de Fourier de las secuencias original y diezmada muestra que esta última es una versión escalada de la primera, lo que enfatiza la naturaleza periódica introducida por la diezmada. Los espectros de la secuencia diezmada difieren del original solo en términos de escala de frecuencia.
Si el espectro original está limitado por la banda y libre de aliasing, la diezmada extiende efectivamente el espectro sobre una banda de frecuencia más grande. Esta dispersión se produce porque la decimación reduce la frecuencia de muestreo en un factor de N. Para evitar el aliasing, es fundamental que la señal original esté sobremuestreada, lo que significa que la frecuencia de muestreo es lo suficientemente alta en relación con el componente de frecuencia más alta de la señal.
En términos prácticos, la decimación de una secuencia derivada de una señal de tiempo continuo también se conoce como submuestreo. Este proceso reduce la velocidad de datos, lo que la hace más manejable y, al mismo tiempo, conserva las características esenciales de la señal original. Cuando la secuencia original se interpreta como muestras de una señal de tiempo continuo, se debe tener en cuenta cuidadosamente el teorema de muestreo para garantizar que no haya pérdida de información debido al aliasing.
La decimación es una técnica valiosa en el procesamiento de señales digitales, que permite un manejo y análisis de datos más eficientes. Al reducir la cantidad de muestras y mantener la información espectral crítica, la decimación permite un procesamiento y transmisión efectivos de señales en diversas aplicaciones, incluidas las telecomunicaciones, el procesamiento de audio y la compresión de datos. Asegurarse de que la señal original esté sobremuestreada adecuadamente antes de la decimación es clave para evitar el aliasing y preservar la integridad de la señal reconstruida.

Reducción de la resolución de muestreo

Considere una secuencia muestreada con valores cero entre instantes de muestreo. Reemplácelo tomando cada N-ésimo valor de la secuencia muestreada.
El original y ...

Education

Educación

JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Sampling

Muestreo

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 pattern.

Decimation also changes the apparent frequency range. If the original signal is band-limited and has no aliasing, the spectrum spreads over a larger frequency band after the sampling rate is reduced by a factor of N. This is why the original signal must be oversampled, meaning the sampling frequency is high enough compared with the signal’s highest frequency component.

When a sequence comes from a continuous-time signal, decimation is also called downsampling. It lowers the data rate while keeping the important features of the signal. Care is needed to follow the sampling theorem, because aliasing can cause information loss. Decimation is widely used in telecommunications, audio processing, and data compression because it helps make signals easier to store, transmit, and analyze.

Decimation and Sampling Rate Reduction

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 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

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 decimation keeps every N-th sample, reduces data rate, and changes the spectrum. See why oversampling helps prevent aliasing.

Decimation and Sampling Rate Reduction | 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

Decimation and Sampling Rate Reduction

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