# rsequence.m

R-sequences described in Malcolm Levitt's review (https://doi.org/10.1002/9780470034590.emrstm0551). The notation below is based on RN_{n}^{\nu}.

## Syntax

[phases,pulse_amp,pulse_dur]=rsequence(n_rotor_periods,n_blocks_per_period,... phase_factor,n_cycle_repeats,mas_rate,... element_type,supercycle_type)

## Arguments

n_rotor_periods - "small n" symmetry number, gives number of rotor periods required in the R symmetry n_blocks_per_period - "capital n" symmetry number, gives the number of R elements contained within the R symmetry phase_factor - "nu" to calculate the alternating phase in the R sequence: 180*nu/N = 180*phase_factor/n_blocks_per_period n_cycle_repeats - number of times the full R sequence is applied mas_rate - rotor spinning rate, Hz element_type - R element needs to be an inversion pulse. Common R elements are: '180_pulse' : simple inversion pulse '90270_pulse' : composite inversion pulse supercycle_type - The R sequence can be repeated multiple times in combination with supercycles, for improved performance, removal of undesired higher order terms. If the he unmodified R is denoted [phase], this can either be in- verted, [-phase], or have an overall phase added to it, [phase]_addph. Common supercycles are: 'hetero_single_quantum' [phase]_0:[-phase]_0:[phase]_120:[-phase]_120:[phase]_240:[-phase]_240 'homo_double_quantum_nucycle' [phase]_0:[-phase]_0 'homo_double_quantum_nupicycle' [phase]_0:[-phase]_0:[-phase]_180:[phase]_180

## Outputs

phases - the sequence of pulse phases, radians pulse_amp - RF nutation frequency in rad/s, a scalar because R-sequences are phase-modulated pulse_dur - duration of the pulses in the sequence element, a vector with the length matching the number of pulses in the sequence element (seconds)

## See also

*Version 2.7, authors: Marina Carravetta, Ilya Kuprov*