Name: sampling narrow frequency bands
Uploaded: 2024-09-26T13:17:07.000Z
Duration: 1 min 17 s
Channel: JoVE

Considere una señal muestreada a una velocidad superior al doble de su frecuencia más alta.
Una señal con la mayor parte de su energía concentrada en una banda de frecuencia estrecha se conoce como señal de paso de banda. La técnica utilizada para el muestreo de estas señales se denomina muestreo de paso de banda.
El espectro de la señal tiene un límite de frecuencia inferior, ω1, que es mayor que su ancho de banda.
El espectro es distinto de cero dentro de las bandas de frecuencia inferior y superior definidas.
Al multiplicar la señal en el dominio del tiempo por un tren de impulsos, se produce una señal muestreada.
El espectro de la señal muestreada se obtiene convolucionando el espectro de la señal con el espectro del tren de impulsos durante 2π.
Esta convolución hace que el espectro de la señal se repita periódicamente con un período de 2π/T.
A medida que T aumenta, el espacio entre las repeticiones disminuye. El solapamiento se produce cuando estos espectros repetidos se superponen.
El aliasing se puede evitar asegurándose de que el espaciado entre los espectros repetidos sea mayor que el ancho de banda de la señal y con el valor máximo de T. 
Los filtros con constantes y frecuencias específicas pasan las frecuencias dentro del rango deseado.

muestreo de paso de banda

En el procesamiento de señales, el muestreo de paso de banda es una técnica eficaz para muestrear señales que tienen la mayor parte de su energía concentrada en una banda de frecuencia estrecha. Este tipo de señal se conoce como señal de paso de banda. El principio clave del muestreo de paso de banda implica muestrear la señal a una velocidad que sea mayor que el doble del ancho de banda de la señal para evitar el aliasing.

Una señal de paso de banda tiene un espectro con un límite de frecuencia inferior, denotado como ω_1, y un límite de frecuencia superior, denotado como ω_2. El espectro es distinto de cero solo dentro de este rango de frecuencia específico. Para muestrear esta señal, la señal del dominio del tiempo se multiplica por un tren de impulsos, lo que da como resultado una señal muestreada. El espectro de esta señal muestreada se obtiene luego convolucionando el espectro original de la señal con el espectro del tren de impulsos en un rango de 2π. Este proceso de convolución hace que el espectro de la señal se repita periódicamente, con un período de 2π/T. Aquí, T es el intervalo de muestreo y, a medida que T aumenta, el espaciado entre estos espectros repetidos disminuye.

El aliasing, un fenómeno en el que se produce la superposición de estos espectros repetidos, se puede evitar garantizando que el espaciado entre los espectros repetidos sea mayor que el ancho de banda de la señal. Esto requiere una selección cuidadosa del valor máximo de T para mantener una separación adecuada entre los espectros repetidos.

En la práctica, se emplean filtros para aislar y dejar pasar frecuencias dentro del rango deseado. Estos filtros tienen constantes y frecuencias específicas diseñadas para permitir que solo pasen las frecuencias dentro de la banda estrecha, preservando así la integridad de la señal original y evitando el aliasing. Este proceso garantiza que la señal se muestree con precisión y se reconstruya sin distorsión.

Muestreo de paso de banda

Considere una señal muestreada a una velocidad superior al doble de su frecuencia más alta.
Una señal con la mayor parte de su energía concentrada en una banda de frecuencia estrecha es ...

Education

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JoVE Core

Electrical Engineering

Ingeniería Eléctrica

Unit 1

Unidad 1

Sampling

Muestreo

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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 creates a sampled signal with repeating spectra.

The sampled signal spectrum is found by convolving the original spectrum with the spectrum of the impulse train over a range of 2π. That convolution makes the spectrum repeat periodically, with a period of 2π/T, where T is the sampling interval. As T increases, the repeated spectra move closer together.

Aliasing happens when those repeated spectra overlap. To avoid it, the spacing between the repeated spectra must stay greater than the signal bandwidth. That means the maximum value of T has to be chosen carefully so the spectra remain separated.

In practice, filters help isolate the desired narrow band. These filters use specific constants and frequencies so only the needed frequencies pass through. This keeps the original signal intact and allows accurate sampling and reconstruction without distortion.

Sampling Narrow Frequency Bands

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

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

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 bandpass sampling captures signals in a narrow frequency band, avoids aliasing, and uses filters to preserve the original signal.

Sampling Narrow Frequency Bands | 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

Sampling Narrow Frequency Bands

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