Phase-Sensitive nD data Processing Tips from Frank Delaglio

(Quoted from Frank Delaglio’s NMRPipe Yahoo group, since migrated to nmrpipe@groups.io)

Greetings, Dear Pipers,

In the various phase-sensitive multidimensional experiments, the real and imaginary parts of the indirect dimensions are generated via separate measurements. Ideally, these are cos(t) for the real part, and -sin(t) for the imaginary part.

Sometimes, ether because of details in the way the data are recorded or converted, the final result will be cos(t) sin(t) instead. When the sign of the imaginary data is wrong in this way, the Fourier transformed data will look reversed. So, in this case, we use “FT -neg” which negates the imaginary data before the transform. Note that this is not exactly equivalent to reversing the spectrum, so that if you find a dimension is reversed, you should reprocess with “FT -neg”, not reverse it using “REV”.

Likewise, some acquisition methods will generate data where the first and second halves of the dimension will be rotated, so that the center of the spectrum is rotated to the edges instead. This corresponds to changing the sign of alternating points in the data. In this case, the data should be transformed using “FT -alt”, which will change the sign of alternating points before transform.

Sometimes, both kinds of manipulation are needed (“FT -neg -alt”).

Note that at first glance, a dimension that needs “FT -alt” might look like it has a mirror image, but a mirror image is something different …

If we were to Fourier transform data that have a real part cos(t), and an imaginary part of zero, the result would have a mirror image; a positive peak on one side would have a positive peak mirror image on the other.

Likewise, if we were to Fourier transform data that have a real part of zero, and an imaginary part of -sin(t), the result would have a negative mirror image; a positive peak on one side will have a negative peak mirror image on the other side.

When real = cos(t) and imaginary = -sin(t) results are combined, one side of the mirror image is canceled; this is how measuring complex data allows us to discriminate between positive and negative frequencies (that is, whether a signal is above or below the center of the spectrum). If the spectral dimensions don’t have cos(t) and sin(t) components that can exactly cancel in this way, the resulting spectrum will have mirror images.

In the case of gradient enhanced data, instead of measuring cos(t) and -sin(t) components, we measure two components that are each mixtures of cos(t) and sin(t). Then, during conversion, we recombine these to generate a final result which has cos(t) for the real part, and -sin(t) for the imaginary part. This recombination is often called “gradient shuffling”, and in NMRPipe, it is performed when a dimension is converted with mode “Echo-AntiEcho” or “Rance-Kay”. If this shuffling is not performed as needed on a gradient-enhanced dimension, a mirror image will result when that dimension is transformed. Likewise, if shuffling is used on a dimension that is not gradient-enhanced, a mirror image will also result.

These issues are made more complicated by interleaved experiments, which can potentially change the organization of data so that corresponding real and imaginary components are no longer adjacent, and this can confound sign manipulation or shuffling, potentially also resulting in mirror images.

When possible, organize interleaved experiments so that quadrature detection loops are “inside” the interleaving loops; this will conserve the relative arrangement of real and imaginary parts. If the interleaving is done in the innermost loop, any gradient shuffling needed might have to be deferred to a later step.

One way to handle such interleaved data is to convert it as a single two-dimensional result with “-yMODE Complex”, and then use the “pseudo3D.com” utility to split it into a 2D series. This utility can also perform the gradient shuffling step if needed.

Here are some rules of thumb:

* If a dimension looks reversed, use “FT -neg” (not REV!).
* If the first and second half of the dimension are rotated, use “FT -alt”.
* Sometimes, both cases (“FT -neg -alt”) are needed.
* If a dimension has an actual mirror image, check -yMODE -zMODE etc during conversion.
* Conversion and shuffling will often introduce a need for an additional +/- 90 degree phase correction.
* Interleaved data might need special handling (see pseudo3D.com).
* Keep quadrature detection loops inside interleave loops when possible.

Cheerful Regards,

big fd

Phase-Sensitive nD data Processing Tips from Frank Delaglio
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