Multiple effective fields created by a periodic irradiation of radiofrequency field in NMR

A theory is presented to calculate multiple effective radiofrequency (RF) fields created by a periodic irradiation of a RF field. It is shown that a periodic irradiation of an RF field to a spin system in a strong magnetic field is equivalent to an irradiation by an infinite number of symmetrically amplitude-scaled and anti-symmetrically phase-shifted RF fields equally spaced in the frequency domain. The sidebands of the excitation profile are therefore symmetrical in amplitude and anti-symmetrical in phase. Applications of the theory to a ω1x|sin(πt/Δτ)| shaped pulse and a DANTE pulse are shown to yield results comparable to Bloch numerical simulations.