Gaussian Pulse Cascades and Selective Two-Dimensional NMR
Novel shaped selective time-domain RF pulses, dubbed “Gaussian pulse cascades” (2) are presented and shown to achieve new standards of frequency-domain selectivity for inversion or in-phase excitation. The response of an isolated spin I = 1/2 system is verified by simulation and experiment. The pulses consist of superpositions of three or four time- shifted Gaussians with optimized widths and peak amplitudes. A modified Simplex optimization algorithm was used to obtain amplitude envelopes having excellent frequency-domain responses from starting pulses which were chosen on the grounds of Fourier transform considerations. The resulting pulses are defined by only 9 or 12 parameters for inversion and excitation respectively.