<?xml version="1.0" encoding="UTF-8"?>
<term>
  <id>08248</id>
  <title>folding</title>
  <longtitle>IUPAC Gold Book - folding</longtitle>
  <doi>10.1351/goldbook.08248</doi>
  <code>08248</code>
  <status>current</status>
  <synonym><em>synonym</em>: aliasing</synonym>
  <definitions>
    <item>
      <id>1</id>
      <text>The appearance of peaks at incorrect frequencies in a mathematically-processed spectrum due to insufficient density of datapoints in the time-domain spectrum or from peaks outside of the sampled frequency range.This process can be simulated by folding a spectrum that shows the correct wavenumbers back onto itself at \(\tilde{\nu}_{\rm{M}}\) and its multiples.</text>
      <notes>
        <item>Folding is a consequence of undersampling in spectroscopy.</item>
        <item>In vibrational spectroscopy, when a spectrum is sampled correctly only up to a wavenumber \(\tilde{\nu}_{\rm{M}}\), radiation of wavenumber \(\tilde{\nu} \gt \tilde{\nu}_{\rm{M}}\) appears to have a wavenumber between 0 and \(\tilde{\nu}_{\rm{M}}\), per the table below:</item>
      </notes>
      <contexts/>
      <links>
        <item>
          <term>Nyquist criterion</term>
          <url>https://goldbook.iupac.org/terms/view/08275</url>
        </item>
        <item>
          <term>undersampling</term>
          <url>https://goldbook.iupac.org/terms/view/08297</url>
        </item>
        <item>
          <term>vibrational spectroscopy</term>
          <url>https://goldbook.iupac.org/terms/view/08708</url>
        </item>
        <item>
          <term>wavenumber</term>
          <url>https://goldbook.iupac.org/terms/view/08301</url>
        </item>
      </links>
      <sources>
        <item>PAC, 2021, 93, 647. 'Glossary of methods and terms used in analytical spectroscopy (IUPAC Recommendations 2019)' on page 659 (https://doi.org/10.1515/pac-2019-0203)</item>
      </sources>
    </item>
  </definitions>
  <altoutputs>
    <html>https://goldbook.iupac.org/terms/view/08248/html</html>
    <json>https://goldbook.iupac.org/terms/view/08248/json</json>
    <plain>https://goldbook.iupac.org/terms/view/08248/plain</plain>
  </altoutputs>
  <citation>Citation: 'folding' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.08248</citation>
  <license>The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms.</license>
  <collection>If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .</collection>
  <disclaimer>The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.</disclaimer>
  <accessed>2026-06-30T21:41:42+00:00</accessed>
</term>
