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Related Concept Videos

Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

203
Signal processing techniques are essential for accurately converting continuous signals to digital formats and vice versa. When a continuous signal is sampled with a period T, the resulting sampled signal exhibits replicas of the original spectrum in the frequency domain, spaced at intervals equal to the sampling frequency. To handle this sampled signal, a zero-order hold method can be applied, which creates a piecewise constant signal by retaining each sample's value until the next...
203
Aliasing01:18

Aliasing

136
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...
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Upsampling01:22

Upsampling

238
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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Sampling Theorem01:15

Sampling Theorem

342
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.
342
Downsampling01:20

Downsampling

158
When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...
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¹³C NMR: ¹H–¹³C Decoupling01:04

¹³C NMR: ¹H–¹³C Decoupling

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The probability of having two carbon-13 atoms next to each other is negligible because of the low natural abundance of carbon-13. Consequently, peak splitting due to carbon-carbon spin-spin coupling is not observed in spectra. However, protons up to three sigma bonds away split the carbon signal according to the n+1 rule, resulting in complicated spectra.
A broadband decoupling technique is used to simplify these complex, sometimes overlapping, signals. Broadband decoupling relies on a...
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Related Experiment Video

Updated: Jul 6, 2025

Applying Hyperspectral Reflectance Imaging to Investigate the Palettes and the Techniques of Painters
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Fast reconstruction of hyperspectral images from coded acquisitions using a separability assumption: erratum.

Elizabeth Hemsley, Ibrahim Ardi, Tony Rouvier

    Optics Express
    |January 5, 2024
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    Summary

    This erratum corrects a minor numerical value in a previous publication. The correction does not alter the study's original findings or conclusions.

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    Area of Science:

    • Optics and Photonics
    • Scientific Publishing

    Background:

    • Previous research published in Optics Express requires a correction.
    • An erratum is necessary to ensure data accuracy.

    Purpose of the Study:

    • To formally correct a specific numerical value in a prior publication.
    • To maintain the integrity of the scientific record.

    Main Methods:

    • Review of the original publication's data.
    • Identification and correction of the erroneous numerical value.

    Main Results:

    • A single numerical value has been corrected.
    • The correction has been verified not to impact overall results.

    Conclusions:

    • The original conclusions remain valid.
    • The publication's findings are unaffected by this numerical correction.