Numerical simulation of periodic nuclear magnetic resonance problems: fastcalculation of carousel averages

Many nuclear magnetic resonance (NMR) problems involve spin evolution in th e presence of a periodic Hamiltonian. In many cases, calculation of the spi n response requires a 'carousel average', meaning a summation of NMR signal s over all cyclic permutations of the perturbation. Symmetry theorems are d erived which in many cases allow this carousel average to be performed with minimal computational effort. This has implications for the computation of NMR spectra under asynchronous decoupling sequences, and for the computati on of powder NMR spectra in the presence of sample rotation. Calculated mag ic-angle spinning powder spectra of L-[C-13(3)] alanine are compared with e xperimental results.