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Related Concept Videos

Aliasing01:18

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 signal...
Bandpass Sampling01:17

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. The spectrum...
Sampling Theorem01:15

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.
Upsampling01:22

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...
Downsampling01:20

Downsampling

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...
Reconstruction of Signal using Interpolation01:10

Reconstruction of Signal using Interpolation

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 sampling...

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ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis
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Nonuniform sampling and spectral aliasing.

Mark W Maciejewski1, Harry Z Qui, Iulian Rujan

  • 1University of Connecticut Health Center, Department of Molecular, Microbial, and Structural Biology, 263 Farmington Ave., Farmington, CT 06030-3305, USA.

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|May 6, 2009
PubMed
Summary
This summary is machine-generated.

Nonuniform sampling in spectral analysis can lead to complex aliasing. Increasing effective bandwidth by random or bursty sampling shifts artifacts, improving spectral quality without penalties.

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Signal Processing

Background:

  • The Nyquist theorem defines sampling intervals for uniform sampling to prevent aliasing.
  • Nonuniform sampling violates the standard Nyquist theorem, leading to complex aliasing phenomena.
  • Spectral artifacts in nonuniformly sampled data can be identified as aliases.

Purpose of the Study:

  • To investigate aliasing in nonuniformly sampled data.
  • To demonstrate how to mitigate aliasing artifacts in spectral analysis.
  • To explore the benefits of nonuniform sampling for improving spectral quality.

Main Methods:

  • Analysis of aliasing phenomena under nonuniform sampling conditions.
  • Determination of effective bandwidth based on sample time distribution.
  • Implementation of random and bursty sampling strategies.
  • Application of nonuniform sampling in the indirect dimension of SOFAST-HMQC experiments.

Main Results:

  • Nonuniform sampling introduces complex aliasing not predicted by the standard Nyquist theorem.
  • Effective bandwidth depends on the actual distribution of sample times, not just grid spacing.
  • Increasing effective bandwidth by random or bursty sampling shifts artifacts out of the spectral window.
  • Nonuniform sampling can achieve benefits of oversampling without time or resolution penalties.

Conclusions:

  • Nonuniform sampling requires advanced aliasing management strategies.
  • Effective bandwidth is a crucial parameter for predicting and mitigating aliasing in nonuniformly sampled data.
  • Nonuniform sampling offers an advantageous approach to enhance spectral quality in NMR experiments like SOFAST-HMQC.