# 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 couple of 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. If an axis contains more points than the other one, Reload the spectrum and reprocess it. This time set the size of the two FTs to identical values. The matrix, after the double FT, will be square and will lend itself to symmetrization.

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 by 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 ⇧-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 lends the auxiliary matrix. The two matrices must have an identical number of points along X and along Y.

### Web articles

Introduction to Covariance NMR

Practical Review