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Related Concept Videos

Fast Fourier Transform01:10

Fast Fourier Transform

1.2K
The Fast Fourier Transform (FFT) is a computational algorithm designed to compute the Discrete Fourier Transform (DFT) efficiently. By breaking down the calculations into smaller, manageable sections, the FFT significantly reduces the computational complexity involved. Direct computation of an N-point DFT requires N2 complex multiplications, whereas the FFT algorithm needs only (N/2)log⁡2N multiplications, offering a much faster performance.
The computational efficiency of the FFT becomes...
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Two-Dimensional (2D) NMR: Overview01:12

Two-Dimensional (2D) NMR: Overview

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The 1D NMR spectrum of large and complex molecules like natural products has complicated splitting patterns and overlapping signals, which can be easily interpreted using 2-dimensional (2D) NMR. Unlike 1D NMR, 2D NMR has two frequency axes that provide the coupling information between the nucleus A and nucleus B in a molecule. The process from which 2D spectra are obtained has four steps.
The first step is the preparation period, during which nucleus A is excited with a radiofrequency pulse....
1.8K
2D NMR: Overview of Homonuclear Correlation Techniques01:16

2D NMR: Overview of Homonuclear Correlation Techniques

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Homonuclear correlation spectroscopy (COSY) is a powerful technique used in Nuclear Magnetic Resonance (NMR) spectroscopy to study the correlations between nuclei of the same type within a molecule. It provides information about scalar couplings between adjacent nuclei, which helps determine connectivity and structural information. There are several COSY variants, each with its unique strengths and experimental parameters.
COSY90 is the standard two-dimensional (2D) COSY experiment that...
808
2D NMR: Overview of Heteronuclear Correlation Techniques01:18

2D NMR: Overview of Heteronuclear Correlation Techniques

910
Heteronuclear correlation spectroscopy is an analytical technique that investigates the coupling between different types of nuclei, often a proton and an X-nucleus, such as carbon-13 or nitrogen-15. This method is commonly used in nuclear magnetic resonance (NMR) spectroscopy to gain insights into complex chemical compounds' structural and compositional aspects. A typical heteronuclear correlation spectrum displays X-nucleus chemical shifts on one axis and a proton spectrum on the other...
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NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences01:17

NMR Spectrometers: Radiofrequency Pulses and Pulse Sequences

2.1K
A pulse is a short burst of radio waves distributed over a range of frequencies that simultaneously excites all the nuclei in the sample. Upon passing a radio frequency pulse along the x-axis, the nuclei absorb energy corresponding to their Larmor frequencies and achieve resonance. This shifts the net magnetization vector from the z-axis toward the transverse plane. This angle of rotation of the magnetization vector, or the flip angle, is proportional to the duration and intensity of the pulse.
2.1K
NMR Spectrometers: Resolution and Error Correction01:14

NMR Spectrometers: Resolution and Error Correction

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When magnetic nuclei in a sample achieve resonance and undergo relaxation, the signal detected in NMR is an approximately exponential free induction decay. Fourier transform of an exponential decay yields a Lorentzian peak in the frequency domain. Lorentzian peaks in an NMR spectrum are defined by their amplitude, full width at half maximum, and position, where the peak width is governed by the spin-spin relaxation time alone. In real experiments, however, the applied magnetic field is rendered...
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Related Experiment Video

Updated: Apr 8, 2026

Measuring Interactions of Globular and Filamentous Proteins by Nuclear Magnetic Resonance Spectroscopy NMR and Microscale Thermophoresis MST
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Fast multi-dimensional NMR acquisition and processing using the sparse FFT.

Haitham Hassanieh1, Maxim Mayzel2, Lixin Shi1

  • 1Massachusetts Institute of Technology, 32 Vassar Street, 32-G936, Cambridge, MA, 02139, USA.

Journal of Biomolecular NMR
|July 1, 2015
PubMed
Summary
This summary is machine-generated.

Sparse fast Fourier transform enables high-dimensional Nuclear Magnetic Resonance (NMR) spectroscopy with reduced measurement times and computational costs. This novel method reconstructs high-quality spectra efficiently, overcoming limitations of traditional techniques.

Keywords:
Compressed sensingFast NMRNon uniform samplingReduced dimensionality

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Area of Science:

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

Background:

  • High-dimensional Nuclear Magnetic Resonance (NMR) experiments offer enhanced spectral resolution and direct insights into atomic interactions.
  • Traditional NMR methods face challenges including lengthy acquisition times, substantial computational demands, and significant data storage requirements.

Purpose of the Study:

  • To introduce a novel signal collection and processing method for NMR spectroscopy.
  • To demonstrate the capability of this new method in reconstructing high-quality, large-dimensionality spectra efficiently.

Main Methods:

  • Development and application of a sparse fast Fourier transform algorithm for NMR signal processing.
  • Utilizing the new algorithm for reconstructing spectra from NMR data.
  • Demonstration on a 4-dimensional (4D) BEST-HNCOCA spectrum.

Main Results:

  • The sparse fast Fourier transform method reconstructs high-quality spectra for large-sized, high-dimensional NMR experiments.
  • Achieves significantly shorter measurement times compared to conventional methods.
  • Requires faster computations and minimal storage for processing sparse spectra.

Conclusions:

  • Sparse fast Fourier transform presents a viable and efficient alternative for high-dimensional NMR data acquisition and processing.
  • This method effectively addresses the limitations of speed, computational power, and storage associated with traditional NMR techniques.
  • Enables more accessible and rapid analysis of complex molecular structures using NMR spectroscopy.