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Monday, May 5, 2008

Nyquist Fold-Back Signals

The Nyquist sampling theorem states that an FID must be sampled at a rate at least twice the highest frequency in the FID in order to faithfully reproduce the correct frequencies in an NMR spectrum. In the FID, the highest frequency is plus or minus 1/2 the spectral width. If a resonance falls within plus or minus 1/2 the spectral width, it will be correctly represented in the spectrum. In the absence of digital filters, if a resonance is outside of the spectral width but within the analog filter band width of the spectrometer, it will still appear in the spectrum but at the wrong frequency (and often with a different phase than the correctly represented resonances). The figure below shows an example of this.The bottom trace is a properly recorded NMR spectrum. The top trace shows a spectrum of the same sample with the spectral width set smaller than necessary to capture all of the peaks. One can see that the resonance outside of the spectral width by delta f is folded into the other side of the spectrum by delta f. This phenomenon is also observed in the indirect dimension of a 2D data set as well as in magnetic resonance images.

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