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

Consider a signal sampled at a rate greater than twice its highest frequency.
A signal with most of its energy concentrated in a narrow frequency band is known as a bandpass signal. The technique used for sampling such signals is called bandpass sampling.
The signal&#39;s spectrum has a lower frequency limit,&#160; &#969;1, &#8203;that is greater than its bandwidth.
The spectrum is nonzero within the defined lower and upper frequency bands.
Multiplying the time-domain signal by an impulse train produces a sampled signal.
The spectrum of the sampled signal is obtained by convolving the signal&#39;s spectrum with the impulse train spectrum over 2&#8203;&#960;.
This convolution causes the signal&#39;s spectrum to repeat periodically with a period of 2&#960;/T.
As T increases, the spacing between the repetitions decreases. Aliasing occurs when these repeated spectra overlap.
Aliasing can be avoided by ensuring the spacing between the repeated spectra is greater than the signal&#39;s bandwidth and with the maximum value of T.&#160;
Filters with specific constants and frequencies pass the frequencies within the desired range.

bandpass sampling

In signal processing, bandpass sampling is an effective technique for sampling signals that have most of their energy concentrated within a narrow frequency band. This type of signal is known as a bandpass signal. The key principle of bandpass sampling involves sampling the signal at a rate that is greater than twice the signal&#39;s bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as &#969;1, and an upper frequency limit, denoted as &#969;2. The spectrum is nonzero only within this specific frequency range. To sample this signal, the time-domain signal is multiplied by an impulse train, resulting in a sampled signal. The spectrum of this sampled signal is then obtained by convolving the signal&#39;s original spectrum with the spectrum of the impulse train over a range of 2&#960;. This convolution process causes the signal&#8217;s spectrum to repeat periodically, with a period of 2&#960;/T. Here, T is the sampling interval, and as T increases, the spacing between these repeated spectra decreases.
Aliasing, a phenomenon where overlapping of these repeated spectra occurs, can be avoided by ensuring that the spacing between the repeated spectra is greater than the signal&#8217;s bandwidth. This requires careful selection of the maximum value of T to maintain adequate separation between the repeated spectra.
In practice, filters are employed to isolate and pass frequencies within the desired range. These filters have specific constants and frequencies designed to allow only the frequencies within the narrow band to pass through, thus preserving the integrity of the original signal while preventing aliasing. This process ensures that the signal is accurately sampled and reconstructed without distortion.

Bandpass Sampling

Consider a signal sampled at a rate greater than twice its highest frequency.
A signal with most of its energy concentrated in a narrow frequency band is ...

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Sampling

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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

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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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