Folding and Aliasing

About

Spectral Aliasing (Figure 1) and Folding (Figure 2) are phenomena in which NMR peaks occur at frequencies that are different from their real frequencies. Such peaks are called folded or aliased peaks, depending on the applied method of data acquisition. The folded or aliased peaks may also appear with sign inversion depending on the acquisition scheme (Figure 1(b) and 2(b)).

Figure 1. Spectral Aliasing. (a) An aliased peak (blue peak) appears at a position in the spectrum that is exactly one spectral width from its real position (dotted peak). (b) Spectral Aliasing with sign inversion.

Figure 2. Spectral Folding. (a) A folded peak (blue peak) appears at the position mirrored about the spectrum boundary, as if you would “fold” the spectrum at the spectrum boundary. (b) Spectral Folding with sign inversion.

Folding and aliasing arise from a trick in FT-NMR, and apply to signals that are outside the selected spectral boundaries. By changing the spectral boundaries, for example by moving the carrier frequency (center of spectrum) and/or changing the spectral width, different peaks can be selected for folding or aliasing. When applying folding or aliasing, it is important to tune the acquisitions parameters such that folded or aliased peaks do not overlap with other peaks and can easily be distinguished from non-folded or non-aliased peaks. A convenient trick to distinguish folded or aliased from non-folded or non-aliased is to cause the peak sign to invert upon folding or aliasing.

Spectral folding or aliasing are typically applied to reduce the recording time while keeping the spectral resolution constant, in particular in 3 or more dimensional NMR where recording time becomes a crucial factor. Good examples are 3D experiments that involve aliphatic carbons, like 13C-NOESY-HSQC or hCCH-TOCSY experiments, of which recording times can be typically reduced by days. In these experiments, convenient use is made of the general correlation between 1H and 13C chemical shifts of aliphatic H-C groups in proteins, which results in empty areas that can be used for aliasing peaks without additional overlap. To illustrate this:

Example

Lets consider a 13C-HSQC of the aliphatic region of a protein. The correlation between the 1H and the 13C chemical shifts for bound H-C groups results in a spectrum with all peaks spread around a pseudo diagonal, leaving the upper left and lower right part of the spectrum empty.

Now, we can apply aliasing in the 13C dimension to reduce the measurement time, whilst keeping the same high resolution. We do this by reducing the spectral width of the 13C dimension:

This causes peaks whose real chemical shifts are outside the new spectral boundaries to appear at the aliased positions in the spectrum, and with inverted peak sign (in this example):

Folding and Aliasing in Analysis

Currently, the functionality to treat folding has not yet been implemented in Analysis, so we restrict ourselves here to a description of how aliased peaks are treated.

In Analysis, it is possible to unaliase an aliased peak by telling the program how the peak was aliased. For example, whether the peak was aliased such that δobs = δ - SW, or δobs = δ + SW.

An important feature of Analysis is that upon unaliasing a peak, it will extend the spectral boundaries of the spectrum beyond the fundamental region to include the real position of the unaliased peak. In addition, in the extended region, Analysis will make a tiled copy of the contours of the original spectrum. These duplications of “ghost” contours may be confusing at first, but have the advantage that a peak can be viewed and picked at its real frequency.

If the unaliased peak is picked, the peak box will automatically be shown on both the aliased and unaliased positions. Analysis distinguishes between aliased peaks and non-aliased peaks by using dashed peak boxes for the aliased peaks.

An aliased peak can always be unaliased by setting the number of spectral widths that have been added to the peak position to move it to its 'real' peak position. This value may be a negative or positive integer and expand the contour to cover the ppm values for the aliased peak.

Minimum and maximum aliased frequencies

When Analysis extends the spectrum bounds, it does so by changing so-called minimum and maximum aliased frequencies of a spectrum. These frequencies can be set independently for each dimension of a spectrum, and be used either to cut off the spectrum contour display at a particular value or to extend the contour display to a particular value.

Example

To illustrate this we look again at the example of a 13C-HSQC of a protein, but now with aliasing. In this case, some aliased peaks (with inverted sign) are located in the upper left part of the spectrum (the dotted region):

In analysis, the aliased peak contours can now be shown at their real frequencies by increasing the Maximum aliased frequency:

The new region in the lower part of the spectrum is a copy of the upper part of the spectrum, resulting in a partly duplicated spectrum.

In this case, it is also possible to remove the aliased peaks from the upper part of the spectrum by increasing the Minimum aliased frequency, which results in a HSQC that now appears as if no aliasing had taken place, and all peaks can be analysed on their real positions: