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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...
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...
IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations01:08

IR Spectrum Peak Splitting: Symmetric vs Asymmetric Vibrations

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...
¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)01:20

¹³C NMR: Distortionless Enhancement by Polarization Transfer (DEPT)

When proton-coupled carbon-13 spectra are simplified by a broadband proton decoupling technique, structural information about the coupled protons is lost. Distortionless enhancement by polarization transfer (DEPT) is a technique that provides information on the number of hydrogens attached to each carbon in a molecule. While the DEPT experiment utilizes complex pulse sequences, the pulse delay and flip angle are specifically manipulated. The resulting signals have different phases depending on...
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...
¹H NMR: Interpreting Distorted and Overlapping Signals01:02

¹H NMR: Interpreting Distorted and Overlapping Signals

Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
As Δν decreases and the signals move closer, the doublets appear increasingly distorted. The intensities of the inner lines increase at the cost of those of the outer lines as the signals are slanted or...

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Updated: May 26, 2026

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis
13:31

High Speed Sub-GHz Spectrometer for Brillouin Scattering Analysis

Published on: December 22, 2015

Phase-sensitive spectral estimation by the hybrid filter diagonalization method.

Hasan Celik1, Clark D Ridge, A J Shaka

  • 1Department of Chemistry, University of California, Irvine, CA 92697-2025, USA. hcelik@uci.edu

Journal of Magnetic Resonance (San Diego, Calif. : 1997)
|January 3, 2012
PubMed
Summary
This summary is machine-generated.

A new Filter Diagonalization Method (FDM) enhances multidimensional NMR spectroscopy using limited data. This robust technique provides accurate phasing, noise floor, and spectral quality assessment for clearer results.

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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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ARL Spectral Fitting as an Application to Augment Spectral Data via Franck-Condon Lineshape Analysis and Color Analysis

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Area of Science:

  • Nuclear Magnetic Resonance (NMR) Spectroscopy
  • Spectroscopic Data Analysis
  • Computational Chemistry

Background:

  • Obtaining high-resolution multidimensional NMR spectra from limited data is challenging.
  • Traditional methods may struggle with phase correction and accurate noise representation.
  • Phase-sensitive spectral estimation is crucial for reliable analysis.

Purpose of the Study:

  • To develop a more robust method for high-resolution multidimensional NMR spectral estimation from limited datasets.
  • To improve phase correction capabilities and accurate noise floor representation.
  • To enhance spectral clarity through line shape transformation.

Main Methods:

  • Application of the Filter Diagonalization Method (FDM) to phase-modulated NMR data.
  • Analysis of data in terms of phase-sensitive Lorentzian peaks.
  • Implementation of regularization techniques to improve linear algebra problem conditioning.
  • Hybrid method for accurate noise floor representation.
  • Lorentzian-to-Gaussian time-domain transformation for line shape enhancement.

Main Results:

  • Successful analysis of phase-modulated data into phase-sensitive spectra.
  • Demonstration that absolute phase information is not required beforehand.
  • Capability for linear phase corrections in each frequency dimension.
  • Improved spectral clarity via Gaussian-like line shape transformation.
  • Accurate representation of the true noise floor and indication of fit quality.

Conclusions:

  • The enhanced FDM offers a robust approach to multidimensional NMR spectral estimation with limited data.
  • The method provides accurate phasing, a true noise floor, and local fit quality assessment.
  • Applicable to n-dimensional NMR data, highlighting the importance of phase-sensitive line shapes.