Hadamard Transform
This operation is intended for data collected with a stochastic pulse sequence in which the phases of the RF pulses differ by 0° or 180°. Transformation matrices are generated from phase lists for stochastic pulse sequences with n=2N-1 pulses. Once generated, the elements of the n-point transformation matrix are stored in a file called Mn.bin in the Hadamard subfolder. Each element is one byte, so those n2-component binary files can be quite large. (The file containing the 2047-pulse transformation matrix is nearly 4MB.) Therefore, only the phase lists are included with the NMR tools installation package, and are stored as ASCII files named Mn.dat . Mn.bin will be created from Mn.dat the first time you apply the Hadamard transform to an n-point data set. Lists for 1 < N < 12 are provided but may need editing in order to match your pulse sequence. Use the Phase Lists | Open submenu command to load a list into a worksheet and compare it with the list for your pulse sequence. (Note that 0° and 180° phases are indicated by 1 and -1, respectively, rather than 0 and 2 as is customary in most pulse sequence programs.) If you need to change the list, use the Save button on the worksheet to export it back to file. The transformation matrix will also be created and exported to Mn.bin.