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Deconvolution, also known as inverse filtering, is the process of extracting the impulse response from known input and output signals. This technique is vital in scenarios where the system's characteristics are unknown, and they must be inferred from the observable signals.
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The distribution law or Nernst's distribution law is the law that governs the distribution of a solute between two immiscible solvents. This law, also known as the partition law, states that if a solute is added to the mixture of two immiscible solvents at a constant temperature, the solute is distributed between the two solvents in such a way that the ratio of solute concentrations in the solvents remains constant at equilibrium.
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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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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.
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Related Experiment Video

Updated: Jan 15, 2026

Proton Transfer and Protein Conformation Dynamics in Photosensitive Proteins by Time-resolved Step-scan Fourier-transform Infrared Spectroscopy
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Deconvoluting Patterson.

Bernhard Rupp1,2

  • 1Department of General, Inorganic and Theoretical Chemistry University of Innsbruck Innrain 80-82 Innsbruck6020 Austria.

Journal of Applied Crystallography
|October 9, 2025
PubMed
Summary
This summary is machine-generated.

Learn about the Patterson function, P(u), an autocorrelation of electron density vital for crystallography. This educational tool simplifies understanding interatomic distances for students in biological and biomedical fields.

Keywords:
1D electron density plotsPatterson functionautocorrelationgraphical animation

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Area of Science:

  • Crystallography
  • Structural Biology
  • Biophysics

Background:

  • The Patterson function, P(u), is a cornerstone in crystallographic data analysis.
  • Its definition as the autocorrelation of electron density presents a conceptual challenge for many students.
  • Understanding autocorrelation is crucial for interpreting P(u) as an interatomic distance map.

Purpose of the Study:

  • To provide an accessible educational resource for understanding the Patterson function and autocorrelation.
  • To simplify the visualization and comprehension of autocorrelation for students in biological and biomedical fields.

Main Methods:

  • Development of a freely available animated PowerPoint slide deck.
  • Utilizes 1D electron density plots and their corresponding autocorrelation to illustrate the Patterson function.
  • Employs animation to intuitively explain the concept of autocorrelation.

Main Results:

  • The animated presentation effectively demonstrates the relationship between electron density and its autocorrelation.
  • The resulting Patterson function is presented as a readily interpretable interatomic distance map.
  • The educational tool enhances intuitive grasp of autocorrelation.

Conclusions:

  • This animated resource simplifies a complex crystallographic concept for a broader audience.
  • It serves as a valuable tool for teaching and learning about the Patterson function and autocorrelation in structural biology.
  • The intuitive approach facilitates understanding of fundamental crystallographic principles.