# Symmetrization of a Square Matrix

Homo-correlated 2D spectra are, in theory, symmetric around the diagonal. This property is exploited to clean the spectrum from noise and artifacts. The operation involved is called symmetrization. It compares couple of points symmetrically placed around the two sides of the diagonal. The higher absolute value is discarded and substituted with (a duplicate of) the lower. The imaginary part has no use after such an operation. It is, therefore, discarded.

iNMR requires the matrix to be square. If it is not, reload the time-domain data and reprocess. This time choose equal FT sizes along f1 and f2.

Symmetrization is much more useful and usable than it is commonly believed. A cosy surely benefits from it, for example, in at least a 99% of cases. If you want to measure integrals, however, consider that integrals of symmetrized spectrum have dubious significance.

# Tilt

Some j-resolved spectra require this correction in frequency along f2. After the tilting all the components of a multiplet are perfectly aligned along f1; they also have an oblique shape which can be corrected by symmetrization. This command is disabled after execution and also when the matrix is square.

# Making J-resolved spectra symmetric

This is straightforward. The spectrum is made symmetric around the central f1 frequency. This command is disabled when the matrix is square.

# removing the t-1 noise

A simple algorithm that can be applied AFTER the correction of the base-plane. Simply select the command “Process/Remove t1 noise”. iNMR first determines the region of pure noise, then measure the level of noise for each row, finally reduces it where it is higher. After this treatment, the level of noise will be constant along all the rows. Only the row that starts with the lowest level of noise is not affected. You can perform symmetrization after the noise-removal, if you like and if the matrix is square.