Pulses with fixed magnitude and variable phase response profiles

The Shinnar-Le Roux (SLR) method of pulse envelope design provides for the generation of nearly arbitrary magnitude response profiles with such great efficiency that the pulse envelopes may often be calculated at the time of sequence initiation. A significant limitation of the method is that it provides only limited control of the phase of the response profile. In the current manuscript it is demonstrated that the phase of the response profile can be modulated without affecting the magnitude profile by replacement of some of the roots of the SLR polynomials with one over their complex conjugate. This method allows interactive tailoring of the phase profile to the user's needs. Although the method does not allow for the optimization of arbitrary phase profiles, a variety of pulses, which are of general utility, have been generated. Some of these pulses and their response profiles are presented.