Frequency-shifted excitation by phase-incremented pulses of arbitrary shape can be solved by introducing a second rotating frame. The results show that a phase-incremented pulse can be decomposed into an infinite number of unsymmetrically amplitude-scaled and phase-shifted effective radio frequency (rf) fields,which are responsible for the unsymmetrical and phase-shifted centerband and sideband excitations. In addition to a universal phase shift associated with each band of excitation, a phase inversion occurs when the scaling factor of the effective rf field becomes negative. Also if the total phase increment of the pulse is not equal to 2k pi (k integer) an additional phase shift equal to the total phase increment will be introduced. By properly choosing the total phase increment the phase shift of the centerband can be compensated. A computer program based on the Bloch equations is developed to calculate directly the excitation profiles of phase-incremented pulses, which agrees well with the theoretical predications.