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Sampling Theorem

Sampling Theorem

In signal processing, the analysis of continuous-time signals, denoted as x(t), often involves sampling techniques to convert these signals into discrete-time signals. This process is essential for digital representation and manipulation. A critical component in sampling is the train of impulses, characterized by the sampling interval and the sampling frequency. The relationship between these parameters and the original signal's properties dictates the success of the sampling process.

Aliasing

Aliasing

Accurate signal sampling and reconstruction are crucial in various signal-processing applications. A time-domain signal's spectrum can be revealed using its Fourier transform. When this signal is sampled at a specific frequency, it results in multiple scaled replicas of the original spectrum in the frequency domain. The spacing of these replicas is determined by the sampling frequency.
If the sampling frequency is below the Nyquist rate, these replicas overlap, preventing the original...

Bandpass Sampling

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's bandwidth to prevent aliasing.
A bandpass signal has a spectrum with a lower frequency limit, denoted as ω1, and an upper frequency limit, denoted as ω2....

Sampling Continuous Time Signal

Sampling Continuous Time Signal

In signal processing, a continuous-time signal can be sampled using an impulse-train sampling technique, followed by the zero-order hold method. Impulse-train sampling involves the use of a periodic impulse train, which consists of a series of delta functions spaced at regular intervals determined by the sampling period. When a continuous-time signal is multiplied by this impulse train, it generates impulses with amplitudes corresponding to the signal's values at the sampling points.
In the...

Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

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Related Experiment Video

Updated: Feb 20, 2026

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Multiplexed coded time domain sampling with metamaterials.

Christian C Nadell, Kebin Fan, Jonathan Y Suen

|October 19, 2017

Summary

This summary is machine-generated.

Researchers developed a new technique using dynamic metamaterial modulators to measure fast, high-frequency signals in the far infrared spectrum. This method allows slow thermal detectors to capture rapid signals, improving imaging system resolution.

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Area of Science:

Physics
Optical Engineering
Materials Science

Background:

Far infrared spectroscopy often relies on thermal detectors with slow response times and low sensitivity.
High-frequency signals in this spectrum are challenging to measure with conventional detectors, necessitating complex alternatives.

Purpose of the Study:

To propose and validate a novel method for measuring high-frequency signals in the far infrared spectrum.
To overcome the limitations of slow thermal detectors in capturing fast-changing signals.

Main Methods:

Utilizing dynamic metamaterial modulators to encode high-frequency signal components into lower frequencies.
Designing an optimal weighing scheme in the time domain for signal encoding.

Main Results:

Successfully demonstrated a method to make high-frequency signals measurable by slow thermal detectors.
Achieved an imaging system with time resolution independent of detector speed.

Conclusions:

The proposed technique enhances the capabilities of thermal detectors for far infrared measurements.
This approach offers a scalable and efficient solution for high-speed signal detection and imaging.