Symmetrization and Covariance NMR
Symmetrization
Homonuclear experiments are, by definition, symmetrical around the diagonal. Actually they seldom are, because the resolution in the direct dimension is usually much higher than in the indirect dimension. Noise and artifacts shouldn't be symmetrical, so you can in theory eliminate them with a symmetrization of the spectrum. This operation compares points symmetrically placed around the two sides of the diagonal. The higher absolute value is discarded and substituted with the lower. The imaginary part has no use after such an operation. It is, therefore, discarded: the matrix becomes real.
You can only apply symmetrization to a square matrix, in theory. In practice, the only requirement is that the spectrometer frequency must be the same along x and y. If the spectral widths or the lengths of the axes are not equal, iNMR will trim the largest one.
Symmetrization has serious drawbacks: the shape of signals becomes square, so they are larger and less separated. Symmetrization can also introduce fake cross-peaks, in case two diagonal signals have intense tails that extend all over the spectrum. Compare the result with the normal spectrum and judge for yourself.
Covariance NMR
A method exists that will yield a square symmetrical matrix starting from any kind of 2-D matrix, even when the two axes are uncorrelated and of different size, even if the ppm scales are drastically different. This computationally-intensive method is called Covariance NMR and was pioneered by Brüschweiler.
In the iNMR implementation, the X axis becomes equal to the Y axis. If you want the opposite, Transpose your spectrum (press Shift-T) before selecting the command Process > Symmetrize > Covariance.
Hybrid Covariance
This is the same algorithm as above. Instead of multiplying the matrix with its own transpose,
it's multiplied with the transpose of another matrix.
In practice, you open two 2-D windows. The window in the foreground is processed.
The window just behind it provides the auxiliary matrix.
The two matrices must have an identical number of points along x and along y.