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.
Notes: - Folding is a consequence of undersampling in spectroscopy.
- 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:
See also: Nyquist criterion
| Range of wavenumber \(\tilde{\nu}\) | \(\tilde{\nu}_{\rm{app}}\) |
|---|
| [\(\tilde{\nu}_{\rm{M}}\), 2\(\tilde{\nu}_{\rm{M}}\)] | 2\(\tilde{\nu}_{\rm{M}}\) - \(\tilde{\nu}\) |
| [2\(\tilde{\nu}_{\rm{M}}\), 3\(\tilde{\nu}_{\rm{M}}\)] | \(\tilde{\nu}\) - 2\(\tilde{\nu}_{\rm{M}}\) |
| [3\(\tilde{\nu}_{\rm{M}}\), 4\(\tilde{\nu}_{\rm{M}}\)] | 4\(\tilde{\nu}_{\rm{M}}\) - \(\tilde{\nu}\) |
| [4\(\tilde{\nu}_{\rm{M}}\), 5\(\tilde{\nu}_{\rm{M}}\)] | \(\tilde{\nu}\) - 4\(\tilde{\nu}_{\rm{M}}\) |
Source:
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)